Chapter 5, Problem 5PEB

The following sound waves have what velocity?

1. a. 20.0 Hz. λ of 17.2 m
2. b. 200.0 Hz, λ of 1.72 m
3. c. 2,000.0 Hz, λ of 17.2 cm
4. d. 20,000.0 Hz. λ of 1.72 cm

To determine

The velocity of the sound wave.

Answer to Problem 5PEB

The velocity of the sound wave is $344\frac{\text{m}}{\text{s}}$.

Explanation of Solution

Write the expression for the velocity of sound wave.

    $v=f\lambda$                                                                                        (I)

Here, $v$ is the velocity of the sound wave, $f$ is the frequency and $\lambda$ is the wavelength.

Conclusion:

Substitute $20.0\text{Hz}$ for $f$ and $17.2\text{m}$ for $\lambda$ in equation (I) to find $v$.

    $\begin{array}{c}v=\left(20.0\text{Hz}\right)\left(17.2\text{m}\right)\\ =\left(20.0\text{Hz}\right)\left(\frac{1{\text{s}}^{-1}}{1\text{Hz}}\right)\left(17.2\text{m}\right)\\ =344\frac{\text{m}}{\text{s}}\end{array}$

Therefore, the velocity of the sound wave is $344\frac{\text{m}}{\text{s}}$.

To determine

The velocity of the sound wave.

Answer to Problem 5PEB

The velocity of the sound wave is $344\frac{\text{m}}{\text{s}}$.

Explanation of Solution

Conclusion:

Substitute $200.0\text{Hz}$ for $f$ and $1.72\text{m}$ for $\lambda$ in equation (I) to find $v$.

    $\begin{array}{c}v=\left(200.0\text{Hz}\right)\left(1.72\text{m}\right)\\ =\left(200.0\text{Hz}\right)\left(\frac{1{\text{s}}^{-1}}{1\text{Hz}}\right)\left(1.72\text{m}\right)\\ =344\frac{\text{m}}{\text{s}}\end{array}$

Therefore, the velocity of the sound wave is $344\frac{\text{m}}{\text{s}}$.

To determine

The velocity of the sound wave.

Answer to Problem 5PEB

The velocity of the sound wave is $344\frac{\text{m}}{\text{s}}$.

Explanation of Solution

Conclusion:

Substitute $2000.0\text{Hz}$ for $f$ and $17.2\text{cm}$ for $\lambda$ in equation (I) to find $v$.

    $\begin{array}{c}v=\left(2000.0\text{Hz}\right)\left(17.2\text{cm}\right)\\ =\left(2000.0\text{Hz}\right)\left(\frac{1{\text{s}}^{-1}}{1\text{Hz}}\right)\left(17.2\text{cm}\times \frac{{10}^{-2}\text{m}}{1.0\text{cm}}\right)\\ =344\frac{\text{m}}{\text{s}}\end{array}$

Therefore, the velocity of the sound wave is $344\frac{\text{m}}{\text{s}}$.

To determine

The velocity of the sound wave.

Answer to Problem 5PEB

The velocity of the sound wave is $344\frac{\text{m}}{\text{s}}$.

Explanation of Solution

Conclusion:

Substitute $20000.0\text{Hz}$ for $f$ and $1.72\text{cm}$ for $\lambda$ in equation (I) to find $v$.

    $\begin{array}{c}v=\left(20000.0\text{Hz}\right)\left(1.72\text{cm}\right)\\ =\left(20000.0\text{Hz}\right)\left(\frac{1{\text{s}}^{-1}}{1\text{Hz}}\right)\left(1.72\text{cm}\times \frac{{10}^{-2}\text{m}}{1.0\text{cm}}\right)\\ =344\frac{\text{m}}{\text{s}}\end{array}$

Therefore, the velocity of the sound wave is $344\frac{\text{m}}{\text{s}}$.