Chapter 5, Problem 5PEA

(a)

To determine

The velocity of the sound wave.

Answer to Problem 5PEA

The velocity of the sound wave is $343\frac{\text{m}}{\text{s}}$.

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 $256\text{Hz}$ for $f$ and $1.34\text{m}$ for $\lambda$ in equation (I) to find $v$.

    $\begin{array}{c}v=\left(256\text{Hz}\right)\left(1.34\text{m}\right)\\ =\left(256\text{Hz}\right)\left(\frac{1{\text{s}}^{-1}}{1\text{Hz}}\right)\left(1.34\text{m}\right)\\ =343.04\frac{\text{m}}{\text{s}}\\ \approx \text{343}\frac{\text{m}}{\text{s}}\end{array}$

Therefore, the velocity of the sound wave is $343\frac{\text{m}}{\text{s}}$.

(b)

To determine

The velocity of the sound wave.

Answer to Problem 5PEA

The velocity of the sound wave is $343\frac{\text{m}}{\text{s}}$.

Explanation of Solution

Conclusion:

Substitute $440.0\text{Hz}$ for $f$ and $78.0\text{cm}$ for $\lambda$ in equation (I) to find $v$.

    $\begin{array}{c}v=\left(440.0\text{Hz}\right)\left(78.0\text{cm}\right)\\ =\left(440.0\text{Hz}\right)\left(\frac{1{\text{s}}^{-1}}{1\text{Hz}}\right)\left(78.0\text{cm}\times \frac{{10}^{-2}\text{m}}{1.0\text{cm}}\right)\\ =343.2\frac{\text{m}}{\text{s}}\\ \approx 343\frac{\text{m}}{\text{s}}\end{array}$

Therefore, the velocity of the sound wave is $343\frac{\text{m}}{\text{s}}$.

(c)

To determine

The velocity of the sound wave.

Answer to Problem 5PEA

The velocity of the sound wave is $343\frac{\text{m}}{\text{s}}$.

Explanation of Solution

Conclusion:

Substitute $750.0\text{Hz}$ for $f$ and $45.7\text{cm}$ for $\lambda$ in equation (I) to find $v$.

    $\begin{array}{c}v=\left(750.0\text{Hz}\right)\left(45.7\text{cm}\right)\\ =\left(750.0\text{Hz}\right)\left(\frac{1{\text{s}}^{-1}}{1\text{Hz}}\right)\left(45.7\text{cm}\times \frac{{10}^{-2}\text{m}}{1.0\text{cm}}\right)\\ =342.75\frac{\text{m}}{\text{s}}\\ \approx 343\frac{\text{m}}{\text{s}}\end{array}$

Therefore, the velocity of the sound wave is $343\frac{\text{m}}{\text{s}}$.

(d)

To determine

The velocity of the sound wave.

Answer to Problem 5PEA

The velocity of the sound wave is $343\frac{\text{m}}{\text{s}}$.

Explanation of Solution

Conclusion:

Substitute $2500.0\text{Hz}$ for $f$ and $13.7\text{cm}$ for $\lambda$ in equation (I) to find $v$.

    $\begin{array}{c}v=\left(2500.0\text{Hz}\right)\left(13.7\text{cm}\right)\\ =\left(2500.0\text{Hz}\right)\left(\frac{1{\text{s}}^{-1}}{1\text{Hz}}\right)\left(13.7\text{cm}\times \frac{{10}^{-2}\text{m}}{1.0\text{cm}}\right)\\ =342.5\frac{\text{m}}{\text{s}}\\ \approx 343\frac{\text{m}}{\text{s}}\end{array}$

Therefore, the velocity of the sound wave is $343\frac{\text{m}}{\text{s}}$.