Chapter 5, Problem 15PEB

The following sound waves have what velocity?

a. 20.0 Hz, $\text{λ}$ of 17.2 m.

b. 200.0 Hz, $\text{λ}$ of 1.72 m.

c. 2,000.0 Hz, $\text{λ}$ of 17.2 cm.

d. 20,000.0 Hz, $\text{λ}$ of 1.72 cm.

To determine

The velocity of the sound waves having frequency and wavelength as $20.0\text{ Hz}$ and $17.2\text{ m}$ respectively.

Answer to Problem 15PEB

Solution:

$344\text{ m/s}$

Explanation of Solution

Given data:

The frequency and wavelength of the sound wavesare $20.0\text{ Hz}$ and $17.2\text{ m}$ respectively.

Formula used:

Write the expression of the velocity of the wave.

$v=\lambda f$

Here, $\lambda$ and $f$ are the wavelength and frequency of the wave.

Explanation:

Calculate the velocity of the sound wave having frequency and wavelength as $20.0\text{ Hz}$ and $17.2\text{ m}$ respectively.

$v_1={\lambda }_1{f}_1$

Here, ${\lambda }_1$ and $f_1$ are the wavelength and frequency of the waves respectively at the given condition.

Substitute $17.2\text{ m}$ for ${\lambda }_1$, and $20.0\text{ Hz}$ for $f_1$.

$\begin{array}{c}{v}_1=\left(17.2\text{ m}\right)\left(20.0\text{ Hz}\right)\\ =\left(17.2\text{ m}\right)\left(20.0{\text{ s}}^{-1}\right)\\ =344\text{ m/s}\end{array}$

Conclusion:

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

To determine

The velocity of the sound waves having frequency and wavelength as $200.0\text{ Hz}$ and $1.72\text{ m}$ respectively.

Answer to Problem 15PEB

Solution:

$344\text{ m/s}$

Explanation of Solution

Given data:

The frequency and wavelength of the sound wavesare $200.0\text{ Hz}$ and $1.72\text{ m}$ respectively.

Formula used:

Write the expression of the velocity of the wave.

$v=\lambda f$

Here, $\lambda$ and $f$ are the wavelength and frequency of the wave.

Explanation:

Calculate the velocity of the sound wave having frequency and wavelength as $200.0\text{ Hz}$ and $1.72\text{ m}$ respectively.

$v_2={\lambda }_2{f}_2$

Here, ${\lambda }_2$ and $f_2$ are the wavelength and frequency of the waves respectively at the given condition.

Substitute $1.72\text{ m}$ for ${\lambda }_2$, and $200.0\text{ Hz}$ for $f_2$.

$\begin{array}{c}{v}_2=\left(1.72\text{ m}\right)\left(200.0\text{ Hz}\right)\\ =\left(1.72\text{ m}\right)\left(200.0{\text{ s}}^{-1}\right)\\ =344\text{ m/s}\end{array}$

Conclusion:

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

To determine

The velocity of the sound waves having frequency and wavelength as $2000.0\text{ Hz}$ and $17.2\text{ cm}$ respectively.

Answer to Problem 15PEB

Solution:

$344\text{ m/s}$

Explanation of Solution

Given data:

The frequency and wavelength of the sound waves are $2000.0\text{ Hz}$ and $17.2\text{ cm}$ respectively.

Formula used:

Write the expression of the velocity of the wave.

$v=\lambda f$

Here, $\lambda$ and $f$ are the wavelength and frequency of the wave.

Explanation:

Calculate the velocity of the sound wave having frequency and wavelength as $2000.0\text{ Hz}$ and $17.2\text{ cm}$ respectively.

$v_3={\lambda }_3{f}_3$

Here, ${\lambda }_3$ and $f_3$ are the wavelength and frequency of the waves respectively at the given condition.

Substitute $17.2\text{ cm}$ for ${\lambda }_3$, and $2000.0\text{ Hz}$ for $f_3$.

$\begin{array}{c}{v}_3=\left(17.2\text{ cm}\right)\left(2000.0\text{ Hz}\right)\\ =\left(17.2\text{ cm}\right)\left(\frac{1\text{ m}}{100\text{ cm}}\right)\left(2000.0{\text{ s}}^{-1}\right)\\ =344\text{ m/s}\end{array}$

Conclusion:

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

To determine

The velocity of the sound waves having frequency and wavelength as $20000.0\text{ Hz}$ and $1.72\text{ cm}$ respectively.

Answer to Problem 15PEB

Solution:

$344\text{ m/s}$

Explanation of Solution

Given data:

The frequency and wavelength of the sound waves are $20000.0\text{ Hz}$ and $1.72\text{ cm}$ respectively.

Formula used:

Write the expression of the velocity of the wave.

$v=\lambda f$

Here, $\lambda$ and $f$ are the wavelength and frequency of the wave.

Explanation:

Calculate the velocity of the sound wave having frequency and wavelength as $20000.0\text{ Hz}$ and $1.72\text{ cm}$ respectively.

$v_4={\lambda }_4{f}_4$

Here, ${\lambda }_4$ and $f_4$ are the wavelength and frequency of the waves respectivelyat the given condition.

Substitute $1.72\text{ cm}$ for ${\lambda }_4$, and $20000.0\text{ Hz}$ for $f_4$.

$\begin{array}{c}{v}_4=\left(1.72\text{ cm}\right)\left(20000.0\text{ Hz}\right)\\ =\left(1.72\text{ cm}\right)\left(\frac{1\text{ m}}{100\text{ cm}}\right)\left(20000.0{\text{ s}}^{-1}\right)\\ =344\text{ m/s}\end{array}$

Conclusion:

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