Physics
Physics
1st Edition
Walker
ISBN: 9780133256925
Textbook solutions

All Solutions

Page 504: Practice Problems

Exercise 22
Step 1
1 of 2
Compute for the frequency of the third harmonic (next higher harmonic for a pipe open at one end).

$$
f_3=3f_1=3(525.0Hz)=1575;Hz
$$

Result
2 of 2
$$
1575;Hz
$$
Exercise 23
Step 1
1 of 3
### Theoretical reminder

We know that the wavelength and frequency determine the speed of a wave. They are related by the following formula:

$$
begin{equation}
v = lambda cdot f
end{equation}
$$

We know that when a standing wave is formed in a bottle or pipe open at one end, the length of the pipe is equal to an odd number of wavelength fourths, that is:

$$
begin{align*}
L = frac{n cdot lambda}{4} , text{ for } , n = 1,3,5 tag{2}
end{align*}
$$

Step 2
2 of 3
### Calculation

Since we know the fundamental frequency to be equal $f = 330text{ Hz}$, and the speed of sound in air to equal $v = 343 ; frac{text{m}}{text{s}}$ the wavelength of the wave can easily be found using formula (1) as follows:

$$
begin{align*}
v = f cdot lambda
end{align*}
$$

Rearranging

$$
begin{align*}
& lambda = frac{v}{f} \
& lambda = frac{343 ; frac{text{m}}{text{s}}}{330text{ Hz}} approx 1.0text{ m}
end{align*}
$$

Now for the length, we know the first harmonic is the one with maximal wavelength, for given pipe distance, knowing this we set the integer $n = 1$, and from formula (2) get:

$$
begin{align*}
L = frac{n cdot lambda}{4}
end{align*}
$$

Using the value for the wavelength we found we get

$$
begin{align*}
L = frac{1 cdot 1.0text{ m}}{4} = 0.25text{ m}
end{align*}
$$

Result
3 of 3
The length of the pipe is $L = 0.25text{ m}$
Exercise 24
Step 1
1 of 2
Use the equation for the wavelength of the third harmonic

$lambda_3=dfrac{4L}{3}$

Solve for L

$$
L=dfrac{3lambda_3}{4}=dfrac{3}{4}(0.22m)=0.17;m
$$

Result
2 of 2
$$
0.17;m
$$
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