## Could you give me the formula for figuring the wavelength of an ultrasound wave?…

#### Could you give me the formula for figuring the wavelength of an ultrasound wave? — BH

The wavelength of any wave is equal to the speed of that wave divided by its frequency. In air, the speed of sound is about 330 meters per second, so an ultrasonic wave with a frequency of 50,000 cycles per second would have a wavelength of about 6.6 millimeters. Since sound travels much faster in liquids or solids, the wavelengths would be larger than in air.

## Are some frequencies of sound more directional than others and, if so, why?

#### Are some frequencies of sound more directional than others and, if so, why? — BKZ, Dayton, OH

In open air, sound waves travel in straight lines regardless of frequency or wavelength. But low frequency (long wavelength) sounds don’t fit well in confined spaces and have less directional character to them. That’s why you only need one subwoofer for a sound system—you can’t hear where the lowest frequency sounds are coming from any way. Higher frequency sounds remain relatively directional, even in confined spaces. The same effects apply to electromagnetic waves—in confined spaces, long wavelength radio waves are effectively less directional than short wavelength light waves.

## What accounts for the difference between two sounds having the same frequency, l…

#### What accounts for the difference between two sounds having the same frequency, loudness, etc. but generated by a guitar and a sitar? — AW, Karachi, Pakistan

Different instruments sound different, even when they play the same notes at the same volumes, primarily because they add different amounts of harmonic tones to their fundamental tones and because these various tones change in volume with time. When you play a note on a guitar, you don’t hear just one pure frequency with a constant volume. Instead, you hear the fundamental frequency and all of the integer multiples of that frequency—the harmonics of that frequency. The relative volumes of those harmonics, and how those volumes change with time, are characteristic of the guitar. If you listen to the same note on a sitar, the relative volumes of the harmonics will be different and you will hear the difference. Because both instruments are plucked, the sounds they emit both start loud and gradually grow softer. If you were to bow their strings, the sound would start soft and gradually grow louder. That’s one reason that you can distinguish a guitar or sitar from a violin.

## How does a violin create sound? Is the sound only made by the strings or is it m…

#### How does a violin create sound? Is the sound only made by the strings or is it made with the help of the violin’s shape and structure? — RH, North York, Ontario

While the vibration of the strings is ultimately responsible for the sounds a violin emits, it is the body of the violin that emits most of that sound. Strings are very poor emitters of sound because they aren’t able to push on the air effectively. When the string moves back and forth through the air, the air simply flows around it to the other side. So instead of compressing and rarefying the air, as it must do in order to produce sound waves, the string just stirs the air around. But the bridge of the violin rocks back and forth as the strings’ vibrate and it conveys this motion to the belly of the violin. The belly moves in and out, compressing and rarefying the air and doing a fine job of producing sound.

## Why does breathing helium make our voices sound Mickey Mouse-ish? Is there anyth…

#### Why does breathing helium make our voices sound Mickey Mouse-ish? Is there anything we can drink that will have the same effect for a longer period? – AP

The pitch of your voice is largely determined by the dimensions of your larynx. That’s why men, with their larger larynxes, generally have lower voices than women. While the sound of your voice originates in the vibrations of your vocal cords, string-shaped objects aren’t very good at emitting sound. Just as a violin employs a box to assist its strings in producing sound, you use your larynx to assist your vocal cords in producing sound. Which pitches your larynx produces well depends on its size and on the speed of sound. Both of these factors are important because the air itself vibrates and either decreasing the size of your larynx or allowing sound to move faster from one side of it to the other will raise the pitch of your voice. Because the speed of sound is much higher in helium (965 m/s) than it is in air (331 m/s), the pitch of your voice rises when you breathe in helium gas. However, as soon as the helium has left your lungs and is replaced by air, your voice returns to normal. Apart from breathing gases with high speeds of sound, there isn’t anything else that will work. You can’t live on pure helium gas, so the only way to sustain this effect would be to breath a helium/oxygen mixture instead of air. Some deep-sea divers do just that and their voices continue to sound “Mickey Mouse-ish” as long as they breathe this mixture.

## What types of sound can humans hear? What types of materials are soundproof? How…

#### What types of sound can humans hear? What types of materials are soundproof? How is the volume of a sound changed? Is the speed of sound the same in all types of media, such as water or air? — JM, Fairfax, VA

In air, sounds are disturbances that consist of compressions and rarefactions—the air molecules are packed either more tightly or less tightly than normal. These regions of too high or too low pressure and density move through the air at about 330 meters per second—the speed of sound and when they pass our ears, we may hear them as sound. As a particular sound passes our ears, the air pressure rises and falls and then rises again, over and over. The number of full cycles—a pressure rise then a pressure fall—that pass our ears each second determines the pitch of the sound we hear. The lowest pitch that our ears are sensitive to is about 20 cycles per second and the highest pitch that we can detect is about 20,000 cycles per second. While other pitches are possible, we simply can’t hear them with our ears.

A sound’s volume is determined by the extent to which the air pressure fluctuates as the sound passes. A loud sound involves a stronger pressure fluctuation than a soft sound. Soundproof materials are ones that decrease the volume of the sound passing through them by weakening the pressure fluctuations. There are two ways to decrease the volume of sound passing through a material: by absorbing the sound or by reflecting it. Soft materials such as carpet or foam rubber absorb sound by allowing the sound’s pressure fluctuations to waste their energies bending the materials. The sound’s energy is converted into thermal energy. Hard, dense materials reflect sounds by making the sounds change speed. Sound travels quickly through most solids and liquids—typically about 5 to 10 kilometers per second. Whenever a wave changes speed in passing from one medium to another, part of that wave is reflected. Thus as sound speeds up in entering a hard surface from the air and as that sound slows down when reentering the air, much of the sound reflects.

## How can glass be shattered with sound?

#### How can glass be shattered with sound? — JI, Rapid City, SD

When sound shatters glass, it breaks the glass in the usual way: by distorting the glass to its breaking point. Whenever glass is bent too far, a crack propagates into the glass from its surface (usually at a defect) and the glass tears. For sound to cause this tearing process, the sound must distort the glass substantially. An extremely loud sound can distort the glass to its breaking point in a single motion. For example, an explosion shatters windows when a surge in air pressure (which you hear as a very loud “pop” sound) exerts so much force on those windows that they bend and break.

However, a moderately loud tone can also break certain glass objects by pushing on those objects rhythmically until they distort beyond their breaking points. To understand how that’s possible, recall that you can get a child swinging strongly on a playground swing either by giving the child one hard push or by giving the child many carefully timed gentle pushes. The gentle pushes transfer energy to the child via a mechanism called resonant energy transfer—the child is exhibiting a natural resonance and you are using that resonance to transfer energy to the child a little bit at a time.

While most glass objects exhibit only very weak natural resonances and are therefore extremely difficult to break via resonant energy transfer, a good crystal wineglass is resonant enough to be broken by a loud tone. You can hear the appropriate tone by flicking the wineglass with your finger. If the wineglass emits a clear bell-like tone, you will be able to break that wineglass by exposing the wineglass to a loud version of that same tone. When the wineglass is exposed to this tone, it begins to vibrate in its natural resonance. Each rise and fall in air pressure associated with the tone adds energy to the vibrating wineglass until its surface is distorting wildly. If the tone is loud enough and its pitch is exactly right, the wineglass will distort a remarkable amount and it may shatter. I know from experience with this effect that the distortion a crystal wineglass can undergo without shattering is amazing—it usually won’t break until it’s upper lip is almost as oval-shaped as an egg. Finding the right tone and holding that tone accurately enough and loudly enough requires sophisticated equipment. Few humans have any chance of breaking a wineglass because the pitch accuracy and volume needed are beyond the abilities of all but the most remarkable opera singers. However, Enrico Caruso was apparently able to do this trick with a wineglass held directly in front of his mouth. Note also that normal window glass and normal drinking glasses are made from soft forms of glass that exhibit no strong resonances—if you tap them, you hear only a dull “thunk” sound, not a bell-like tone. As a result, you can’t break them with tones.

## Why does white noise cancel out the wide range of frequencies in the real world?…

#### Why does white noise cancel out the wide range of frequencies in the real world? What range of frequencies does this technology affect? Can you block out the low thud of a neighbor walking in the unit above yours? — EH, Chelmsford, MA

In the context of sound, a source of white noise emits random, non-repetitive sound waves that have equal acoustic powers at all frequencies. That means that the source emits the same amount of energy each second at each frequency, over the entire audible spectrum. What white noise does is to numb your hearing by creating a featureless, uniform background noise at every frequency you can hear. Since your sensitivity to sound volume is logarithmic, meaning that the acoustic power in a sound has to double before you notice that it’s substantially louder, this uniform background makes it extremely difficult for you to hear small sounds. Regardless of a small sound’s frequencies, the white noise is already exposing your ears to those frequencies and the small sound only makes a small change in the volumes of these frequencies. For an analogy, think about how much more you would notice a small blinking red light in the dark than in bright white sunlight. Similarly, white noise creates the acoustic equivalent of white illumination, making it hard for you to notice small noises that would be very easy to hear against complete silence. If the sounds your neighbor makes are small enough, this numbing effect should make them much less noticeable.

There are also much more sophisticated devices that really cancel noise out. However, these look like earphones and must be worn directly on your ears. These devices use microphones to measure the pressure fluctuations in the sounds and then cause the earphones to create exactly the opposite pressure fluctuations. With these noise cancellation devices properly adjusted, the air pressure fluctuations that are sound never reach your ears at all—they are simply cancelled away to nothing before they arrive.

## How can you make noise by running your finger (if it’s wet) along the rim of a g…

#### How can you make noise by running your finger (if it’s wet) along the rim of a glass?

If you run your damp finger lightly along the rim of a crystal glass, it should begin vibrating. This trick involves a resonant transfer of energy in which your finger rhythmically pushes on the glass to make it vibrate more and more strongly. It takes a delicate touch. If you press to hard, you will prevent the glass from vibrating. If you press too lightly, you won’t give it any energy. Your finger must stick and slip alternately, just as a bow does while sliding across a violin string.