Q: A student blows across the top of a partially filled bottle and produces a sound of frequency 440 Hz. If the speed of sound in air is $$v = 343 \ \mathrm{m/s}$$, and the bottle acts as a closed-end air column, what is the approximate height of the air column in the bottle?

$$h = \frac{v}{4f} = \frac{343}{4 \times 440} = 0.195 \ \mathrm{m}$$

Q: A bottle is filled with water so that the air column above the water is 0.195 m. If the speed of sound is $$343 \ \mathrm{m/s}$$, what is the fundamental frequency produced when blowing across the top?

$$f = \frac{343}{4 \times 0.195} = 440 \ \mathrm{Hz}$$

Q: A student tightens a guitar string, increasing its tension by a factor of 4. If the original frequency was 220 Hz, what is the new frequency?

$$f_{new} = 220 \times \sqrt{4} = 440 \ \mathrm{Hz}$$

Q: A bottle produces a note of 440 Hz when blown across. If the speed of sound increases to $$350 \ \mathrm{m/s}$$ due to temperature, what must the new length of the air column be to maintain the same frequency?

$$L = \frac{350}{4 \times 440} = 0.199 \ \mathrm{m}$$

Q: A closed-end air column resonates at 440 Hz. What is the next higher resonance frequency for this column?

$$f_3 = 3$$ \times 440 = 1320 \ \mathrm{Hz}$$

Question 1

A student blows across the top of a partially filled bottle and produces a sound of frequency 440 Hz. If the speed of sound in air is $$v = 343 \ \mathrm{m/s}$$, and the bottle acts as a closed-end air column, what is the approximate height of the air column in the bottle?

Accepted Answer

$$h = \frac{v}{4f} = \frac{343}{4 	imes 440} = 0.195 \ \mathrm{m}$$

Question 2

If the frequency of the sound produced by blowing across a bottle increases, what happens to the height of the water in the bottle?

Accepted Answer

The height of the water increases, decreasing the length of the air column.

Question 3

A guitar string is tuned to 440 Hz. If the tension in the string is doubled, what happens to the frequency of the sound produced?

Accepted Answer

The frequency increases by a factor of $$\sqrt{2}.$$

Question 4

Which equation correctly gives the fundamental frequency of a closed-end air column of length $$L$$?

Accepted Answer

$$f_1$$ = \frac{v}{4L}$$

Question 5

A bottle is filled with water so that the air column above the water is 0.195 m. If the speed of sound is $$343 \ \mathrm{m/s}$$, what is the fundamental frequency produced when blowing across the top?

Accepted Answer

$$f = \frac{343}{4 	imes 0.195} = 440 \ \mathrm{Hz}$$

Question 6

If a guitar string is shortened while keeping the tension and mass per unit length constant, what happens to the frequency of the sound produced?

Accepted Answer

The frequency increases.

Question 7

A student tightens a guitar string, increasing its tension by a factor of 4. If the original frequency was 220 Hz, what is the new frequency?

Accepted Answer

$$f_{new} = 220 	imes \sqrt{4} = 440 \ \mathrm{Hz}$$

Question 8

Which of the following changes will decrease the frequency of a vibrating string, assuming all other factors remain constant?

Accepted Answer

Increasing the mass per unit length of the string.

Question 9

A bottle produces a note of 440 Hz when blown across. If the speed of sound increases to $$350 \ \mathrm{m/s}$$ due to temperature, what must the new length of the air column be to maintain the same frequency?

Accepted Answer

$$L = \frac{350}{4 	imes 440} = 0.199 \ \mathrm{m}$$

Question 10

If the frequency of a vibrating string is given by $$f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$$, what happens to the frequency if the length $$L is $$doubled and the tension $$T is $$quadrupled?

Accepted Answer

The frequency remains unchanged.

Question 11

A closed-end air column resonates at 440 Hz. What is the next higher resonance frequency for this column?

Accepted Answer

$$f_3 = 3$$ 	imes 440 = 1320 \ \mathrm{Hz}$$

Question 12

Which of the following best explains why tightening a guitar string raises its pitch?

Accepted Answer

Increasing the tension increases the wave speed, which increases the frequency.

Question 13

A bottle is filled so that the air column is 0.15 m long. What is the fundamental frequency if the speed of sound is $$340 \ \mathrm{m/s}$$?

Accepted Answer

$$f = \frac{340}{4 	imes 0.15} = 567 \ \mathrm{Hz}$$

Question 14

If a guitar string is replaced with a heavier string of the same length and tension, what happens to the frequency?

Accepted Answer

The frequency decreases.

Question 15

A closed-end air column has a fundamental frequency of 330 Hz. What is the length of the air column if the speed of sound is $$330 \ \mathrm{m/s}$$?

Accepted Answer

$$L = \frac{330}{4 	imes 330} = 0.25 \ \mathrm{m}$$

Study Notes: Applications of Waves and Sound in Physics

Study Guide - Practice Questions

Study Guide - Flashcards