Q: A sound wave has an intensity of $$1 \times 10$$^{-6}$$ W/m^2$. If the threshold of hearing is 1$$ \times $$10^{-12} W/m$^2$$, what is the sound level in decibels?

$$L = 10 \log \left( \frac{1 \times 10$$^{-6}$$}{1 \times 10$$^{-12}$$} \right) = 120 dB$$

Question 1

Which of the following best describes the difference between transverse and longitudinal waves?

Accepted Answer

In transverse waves, particle motion is perpendicular to the direction of wave propagation, while in longitudinal waves, it is parallel.

Question 2

A guitar string is plucked, producing a sound. If the tension in the string is increased, what happens to the frequency of the fundamental mode?

Accepted Answer

The frequency increases because the wave speed increases.

Question 3

Which equation correctly relates the speed $$v$$, frequency $$f$$, and wavelength $$\lambda of a $$wave?

Accepted Answer

$$v = f \lambda$$

Question 4

A sound wave travels through air and its intensity decreases as the distance from the source increases. Which mathematical relationship best describes this decrease?

Accepted Answer

Intensity decreases as $$\frac{1}{r^2$}$$

Question 5

The loudness of a sound is measured in decibels (dB). Which formula is used to calculate the sound level in decibels?

Accepted Answer

$$L = 10 \log \left( \frac{I}{I_0$} \right)$$

Question 6

A tube open at both ends supports standing waves. What is true about the displacement at the ends of the tube?

Accepted Answer

There are displacement antinodes at both ends.

Question 7

A tube closed at one end and open at the other supports standing waves. What is true about the displacement at the closed end?

Accepted Answer

There is a displacement node at the closed end.

Question 8

Which phenomenon explains why two musical notes of slightly different frequencies played together produce a 'beating' sound?

Accepted Answer

Superposition

Question 9

According to Fourier’s theorem, any complex periodic wave can be represented as:

Accepted Answer

A sum of sinusoidal waves with different amplitudes, frequencies, and phases.

Question 10

A violin and a trumpet play the same note at the same loudness. Why do they sound different?

Accepted Answer

They have different overtone strengths and harmonic content.

Question 11

The audible range for humans is approximately:

Accepted Answer

20 Hz to 20,000 Hz

Question 12

If two sound waves of frequencies $$f_1$$ and $$f_2$$ interfere, what is the beat frequency produced?

Accepted Answer

$$|f_1$ - f_2$|$$

Question 13

Which of the following statements about sound waves is correct?

Accepted Answer

Sound waves require a medium to propagate.

Question 14

A standing wave on a string fixed at both ends has nodes and antinodes. What is true at a node?

Accepted Answer

The amplitude is always zero.

Question 15

The second harmonic frequency $$f_2 of a $$string fixed at both ends is related to the fundamental frequency $$f_1 by$$:

Accepted Answer

$$f_2 = 2f_1$

Question 16

Which property of a sound wave is most closely related to its perceived pitch?

Accepted Answer

Frequency

Question 17

A sound wave has an intensity of $$1 	imes 10$$^{-6}$$ W/m^2$. If the threshold of hearing is 1$$ 	imes $$10^{-12} W/m$^2$$, what is the sound level in decibels?

Accepted Answer

$$L = 10 \log \left( \frac{1 	imes 10$$^{-6}$$}{1 	imes 10$$^{-12}$$} ight) = 120 dB$$

Question 18

Which of the following is an example of a longitudinal wave?

Accepted Answer

Sound wave in air

Question 19

A piano and a clarinet play the same note at the same loudness. What physical property of the sound waves causes them to sound different?

Accepted Answer

The relative strengths of the overtones (harmonics)

Question 20

Which statement about the principle of superposition is correct?

Accepted Answer

The displacement at any point is the vector sum of the displacements of all waves passing through that point.

Waves, Sound, and Superposition: Physics Study Notes

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