All Solutions

Exercise 19

Step 1

1 of 2

The bottle can be modeled as an pipe open at one and end but closed at the other.

Hence, the equation for fundamental frequency (n=1) is

$$
f_1=dfrac{nv}{4L}=dfrac{(1)(343m/s)}{4(0.22;m)}=390;Hz
$$

Result

2 of 2

390 Hz

Exercise 20

Step 1

1 of 2

The bottle can be modeled as a pipe open at one end but closed at the other. Hence, the third harmonic (n=3) can be obtained as

$$
f_3=dfrac{3v}{4L}=dfrac{3(343m/s)}{4(0.18;m)}=1.4;kHz
$$

Result

2 of 2

$$
1.4;kHz
$$

Exercise 21

Step 1

1 of 2

For standing waves in a pipe that is closed at one end, the wavelength of the fundamental frequency is $lambda=4L$

Therefore

$$
L=dfrac{lambda}{4}=dfrac{0.88;m}{4}=0.22;m
$$

Result

2 of 2

$$
0.22;m
$$

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