Waves and Sound — Practice Quiz

A Physics cheat sheet for Waves and Sound — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Wave Speed: Speed \(v\) equals frequency \(f\) times wavelength \(\lambda\).

$$v = f \lambda$$

Linear Density: Mass \(m\) per unit length \(L\) of a string.

$$\mu = \frac{m}{L}$$

Speed of Wave on String: Depends on tension \(F\) and linear density \(m/L\).

$$v = \sqrt{\frac{F}{m/L}}$$

Sound Intensity: Power \(P\) passing perpendicularly through area \(A\).

$$I = \frac{P}{A}$$

Intensity of Spherical Source: Intensity at distance \(r\) from a source emitting power \(P\) uniformly in all directions.

$$I = \frac{P}{4\pi r^2}$$

Sound Intensity Level (Decibels): \(\beta\) in decibels (dB) relative to threshold intensity \(I_0\).

$$\beta = (10 \text{ dB}) \log(\frac{I}{I_0})$$

Where: \(I_0 = 1.00 \times 10^{-12} W/m^2\)

Doppler Effect: Observed frequency \(f_o\) due to relative motion of observer (\(v_o\)) and source (\(v_s\)). \(v\) is speed of sound.

$$f_o = f_s (\frac{1 \pm v_o/v}{1 \mp v_s/v})$$

Where: Top signs: observer towards source / source towards observer

Practice quiz

  1. A wave has a frequency of $500 \text{ Hz}$ and a wavelength of $0.6 \text{ m}$. What is its speed?

    • $300 \text{ m/s}$
    • $833.3 \text{ m/s}$
    • $0.0012 \text{ m/s}$
    • $500.6 \text{ m/s}$

    Answer: $300 \text{ m/s}$

  2. A string of length $2.5 \text{ m}$ has a mass of $0.05 \text{ kg}$. What is its linear density?

    • $0.02 \text{ kg/m}$
    • $0.125 \text{ kg/m}$
    • $50 \text{ kg/m}$
    • $2.55 \text{ kg/m}$

    Answer: $0.02 \text{ kg/m}$

  3. A string with a linear density of $0.01 \text{ kg/m}$ is under a tension of $100 \text{ N}$. What is the speed of a transverse wave on this string?

    • $100 \text{ m/s}$
    • $10 \text{ m/s}$
    • $1000 \text{ m/s}$
    • $1 \text{ m/s}$

    Answer: $100 \text{ m/s}$

  4. A sound source emits $0.01 \text{ W}$ of power uniformly over an area of $0.5 \text{ m}^2$. What is the sound intensity?

    • $0.02 \text{ W/m}^2$
    • $0.005 \text{ W/m}^2$
    • $50 \text{ W/m}^2$
    • $0.51 \text{ W/m}^2$

    Answer: $0.02 \text{ W/m}^2$

  5. A spherical sound source emits $10 \text{ W}$ of power uniformly in all directions. What is the intensity of the sound at a distance of $2 \text{ m}$ from the source?

    • $\frac{10}{16\pi} \text{ W/m}^2$
    • $\frac{10}{4\pi} \text{ W/m}^2$
    • $\frac{10}{2\pi} \text{ W/m}^2$
    • $\frac{10}{8\pi} \text{ W/m}^2$

    Answer: $\frac{10}{16\pi} \text{ W/m}^2$

  6. What is the sound intensity level in decibels for a sound with intensity $I = 1.0 \times 10^{-6} \text{ W/m}^2$? Use $I_0 = 1.00 \times 10^{-12} \text{ W/m}^2$.

    • $60 \text{ dB}$
    • $6 \text{ dB}$
    • $10^{-6} \text{ dB}$
    • $10 \text{ dB}$

    Answer: $60 \text{ dB}$

  7. A car horn emits a sound of frequency $f_s$. If the car is moving towards a stationary observer, how does the observed frequency $f_o$ compare to $f_s$?

    • $f_o > f_s$
    • $f_o < f_s$
    • $f_o = f_s$
    • It depends on the speed of sound.

    Answer: $f_o > f_s$

  8. A string of length $0.5 \text{ m}$ and mass $0.002 \text{ kg}$ is under a tension of $80 \text{ N}$. If a wave on this string has a wavelength of $0.2 \text{ m}$, what is its frequency?

    • $\approx 707 \text{ Hz}$
    • $\approx 354 \text{ Hz}$
    • $\approx 1414 \text{ Hz}$
    • $\approx 283 \text{ Hz}$

    Answer: $\approx 707 \text{ Hz}$

  9. A point source emits sound with a power of $0.04\pi \text{ W}$. What is the sound intensity level in decibels at a distance of $1 \text{ m}$ from the source? Use $I_0 = 1.00 \times 10^{-12} \text{ W/m}^2$.

    • $100 \text{ dB}$
    • $80 \text{ dB}$
    • $120 \text{ dB}$
    • $90 \text{ dB}$

    Answer: $100 \text{ dB}$

  10. A train horn emits a sound at $400 \text{ Hz}$. The train is approaching a stationary observer at $30 \text{ m/s}$. If the speed of sound in air is $340 \text{ m/s}$, what is the observed frequency?

    • $\approx 439 \text{ Hz}$
    • $\approx 365 \text{ Hz}$
    • $\approx 400 \text{ Hz}$
    • $\approx 471 \text{ Hz}$

    Answer: $\approx 439 \text{ Hz}$

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