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Chapter 16: Problem 20

If you blow air across the mouth of an empty soda bottle, you hear a tone. Why is it that if you put some water in the bottle, the pitch of the tone increases?

Short Answer

Expert verified
Answer: The pitch of the tone increases when water is added to a soda bottle and air is blown across its mouth because the effective length of the air column inside the bottle decreases, which in turn increases the resonance frequency of the bottle. Higher resonance frequencies lead to higher pitch tones, thus explaining the observed change in pitch.

Step by step solution

01

Understand resonance frequency and standing waves

When air is blown across the mouth of the bottle, it creates a disturbance in the air column inside the bottle. This disturbance travels down the bottle and reflects back up, causing a series of waves to form within the bottle. The constructive interference of these waves results in a standing wave with a specific frequency known as the resonance frequency. The resonance frequency determines the pitch of the tone heard.
02

Examine how the effective length of the bottle changes with water

When water is poured into the bottle, the air column inside it gets shorter. This reduction in the effective length of the air column leads to a change in the resonance frequency. The resonance frequency can be related to the length of the bottle by the formula f = v / (4 * L), where f is the resonance frequency, v is the speed of sound in the air, and L is the effective length of the bottle.
03

Calculate the new resonance frequency

As water is added to the bottle, the effective length L of the air column inside the bottle decreases. Now, when the equation f = v / (4 * L) is evaluated for this new length, a higher resonance frequency is observed. This new resonance frequency corresponds to a higher tone, and therefore, the pitch of the sound increases.
04

Understand the relationship between pitch and resonance frequency

The pitch of a sound is determined by its frequency. Higher frequency waves result in higher pitch tones, while lower frequency waves produce lower pitch tones. As the resonance frequency increases due to the added water in the bottle, the pitch of the produced tone also increases. In conclusion, when water is added to a soda bottle and air is blown across its mouth, the pitch of the resulting tone increases because the effective length of the air column inside the bottle decreases, which in turn increases the resonance frequency of the bottle. Higher resonance frequencies lead to higher pitch tones, thus explaining the observed change in pitch.

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Most popular questions from this chapter

Two identical half-open pipes each have a fundamental frequency of \(500 .\) Hz. What percentage change in the length of one of the pipes will cause a beat frequency of \(10.0 \mathrm{~Hz}\) when they are sounded simultaneously?

Two trains are traveling toward each other in still air at \(25.0 \mathrm{~m} / \mathrm{s}\) relative to the ground. One train is blowing a whistle at \(300 .\) Hz. The speed of sound is \(343 \mathrm{~m} / \mathrm{s}\). a) What frequency is heard by a man on the ground facing the whistle-blowing train? b) What frequency is heard by a man on the other train?

On a windy day, a child standing outside a school hears the school bell. If the wind is blowing toward the child from the direction of the bell, will it alter the frequency, the wavelength, or the velocity of the sound heard by the child?

In a suspense-thriller movie, two submarines, \(X\) and Y, approach each other, traveling at \(10.0 \mathrm{~m} / \mathrm{s}\) and \(15.0 \mathrm{~m} / \mathrm{s}\), respectively. Submarine X "pings" submarine Y by sending a sonar wave of frequency \(2000.0 \mathrm{~Hz}\). Assume that the sound travels at \(1500.0 \mathrm{~m} / \mathrm{s}\) in the water. a) Determine the frequency of the sonar wave detected by submarine Y. b) What is the frequency detected by submarine \(X\) for the sonar wave reflected off submarine Y? c) Suppose the submarines barely miss each other and begin to move away from each other. What frequency does submarine Y detect from the pings sent by X? How much is the Doppler shift?

A classic demonstration of the physics of sound involves an alarm clock in a bell vacuum jar. The demonstration starts with air in the vacuum jar at normal atmospheric pressure and then the jar is evacuated to lower and lower pressures. Describe the expected outcome.
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