Q: A sound has an intensity $$I = 1.0 \times 10$$^{-8}$$ \text{ W/m}^2. $$What is its sound intensity level in decibels (dB)? Use $$I_0 = 1.0$$ \times $$10^{-12}$$ \text{ W/m}^2$$.

$$\beta = 10 \log_{10} \left(\frac{1.0 \times 10$$^{-8}$$}{1.0 \times 10$$^{-12}$$}\right) = 40 \text{ dB}$$

Question 1

Which of the following statements correctly distinguishes between transverse and longitudinal waves?

Accepted Answer

In transverse waves, particles of the medium move perpendicular to the direction of wave travel; in longitudinal waves, they move parallel.

Question 2

A sound wave travels through air. Which equation best describes the speed of sound in a gas?

Accepted Answer

$$v = \sqrt{\frac{\gamma RT}{M}}$$

Question 3

A sinusoidal wave is described by $$y(x,t) = A \cos \left(2\pi \left(\frac{x}{\lambda} + \frac{t}{T}\right)\right). $$What is the period $$T of $$the wave in terms of its frequency $$f$$?

Accepted Answer

$$T = \frac{1}{f}$$

Question 4

The intensity $$I of a $$spherical wave is given by $$I = \frac{P_{	ext{source}}}{4\pi r^2$}. If $$the distance from the source doubles, what happens to the intensity?

Accepted Answer

It decreases by a factor of 4.

Question 5

A sound has an intensity $$I = 1.0 	imes 10$$^{-8}$$ 	ext{ W/m}^2. $$What is its sound intensity level in decibels (dB)? Use $$I_0 = 1.0$$ 	imes $$10^{-12}$$ 	ext{ W/m}^2$$.

Accepted Answer

$$\beta = 10 \log_{10} \left(\frac{1.0 	imes 10$$^{-8}$$}{1.0 	imes 10$$^{-12}$$}ight) = 40 	ext{ dB}$$

Question 6

A stationary observer hears a frequency $$f'$$ from a source moving away at speed $$v_s. $$Which equation gives the observed frequency?

Accepted Answer

$$f' = \frac{f_s}{1 + \frac{v_s}{v}}$$

Question 7

A Doppler ultrasound probe emits at $$f = 5.0 	ext{ MHz}$$ and detects a maximum frequency shift of $$\Delta f = 400 	ext{ Hz}$$ from blood moving in an artery. If the speed of sound in tissue is $$v = 1540 	ext{ m/s}$$, what is the maximum speed of the blood?

Accepted Answer

$$v = \frac{1}{2} \frac{\Delta f}{f} v = \frac{1}{2} \frac{400}{5.0 	imes 10^6$} 	imes 1540 \approx 0.062 	ext{ m/s}$$

Question 8

Which of the following best describes the principle of superposition?

Accepted Answer

The displacement at a point is the sum of the displacements due to each individual wave.

Question 9

Constructive interference occurs when:

Accepted Answer

The waves are in phase and their amplitudes add.

Question 10

A standing wave on a string has nodes at both ends. If the string length is $$L$$, what is the wavelength $$\lambda of $$the $$m-th $$mode?

Accepted Answer

$$\lambda = \frac{2L}{m}$$

Question 11

For a string of length $$L$$ fixed at both ends, the fundamental frequency $$f_1 is $$given by:

Accepted Answer

$$f_1$$ = \frac{v}{2L}$$

Question 12

A stringed instrument has strings of equal length and tension, but different linear densities. Which property determines the difference in their fundamental frequencies?

Accepted Answer

The linear density $$\mu of $$the string.

Question 13

A standing sound wave in an open-closed tube of length $$L$$ has its fundamental frequency at:

Accepted Answer

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

Question 14

Which of the following is true about nodes and antinodes in a standing wave?

Accepted Answer

Nodes are points of zero displacement; antinodes are points of maximum displacement.

Question 15

A shock wave is produced when:

Accepted Answer

A source moves faster than the wave speed in the medium.

Question 16

In a tube open at both ends, the allowed standing wave frequencies are:

Accepted Answer

$$f_m = m \frac{v}{2L}$$, where $$m = 1, 2, 3, ...$$

Question 17

A standing wave on a string has nodes at $$x = 0$$ and $$x = L. If $$the distance between successive nodes is $$d$$, what is the wavelength?

Accepted Answer

$$\lambda = 2d$$

Question 18

Which of the following best describes destructive interference?

Accepted Answer

It occurs when crests align with troughs, resulting in reduced or zero displacement.

Question 19

A laser cavity establishes standing electromagnetic waves between two parallel mirrors. What boundary condition must be satisfied at the mirrors?

Accepted Answer

There must be a node at each mirror.

Superposition and Standing Waves: Physics for Life Sciences I (Lecture 27, Sections 16.1–16.4)

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