PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 11, Problem 74P

(a)

To determine

The three lowest standing wave frequencies.

(a)

Expert Solution
Check Mark

Answer to Problem 74P

The three lowest standing wave frequencies is f2=600.0Hz, f3=900.0Hz, and f4=1.200kHz.

Explanation of Solution

Write the equation for lowest standing wave frequency.

fn=nv2L (I)

Here, fn is the fundamental frequency, n is the harmonic number, v is the speed of the sound wave, and L is the length of the string.

Conclusion:

The first lowest fundamental frequency of the standing wave is.

f1=300.0Hz

The second lowest fundamental frequency of the standing wave is.

f2=2f1 (II)

Substitute 300.0Hz for f1 in equation (II).

f2=2(300.0Hz)=600.0Hz

The third lowest fundamental frequency of the standing wave is.

f3=3f1 (III)

Substitute 300.0Hz for f1 in equation (III).

f3=3(300.0Hz)=900.0Hz

The fourth lowest fundamental frequency of the standing wave is.

f4=4f1 (IV)

Substitute 300.0Hz for f1 in equation (IV).

f4=4(300.0Hz)=1200.0Hz=1.200×103Hz(103Hz1kHz)=1.200kHz

The pattern for the each situation for the three lowest standing wave frequencies is.

npatternnf1
2N   A   N   A   N600.0Hz
3N A N A N A N900.0Hz
4NANANANAN1.200Hz

Therefore, the three lowest standing wave frequencies is f2=600.0Hz, f3=900.0Hz, and f4=1.200kHz.

(b)

To determine

The four lowest standing wave frequencies, when the strings press light.

(b)

Expert Solution
Check Mark

Answer to Problem 74P

The four lowest standing wave frequencies is f2=600.0Hz, f4=1.200kHz, f6=1.800kHz, and f8=2.400kHz.

Explanation of Solution

Write the equation for lowest standing wave for fundamental frequency.

fn=nf1 (V)

Here, fn is the fundamental frequency for nth harmonic, n is the harmonic number, and f1 is the fundamental frequency.

Conclusion:

The lowest fundamental frequency of the standing wave is.

f1=300.0Hz

Here, the lowest frequency is starts from f2 and only even harmonics are allowed.

The first lowest fundamental frequency of the standing wave is.

f2=2f1 (VI)

Substitute 300.0Hz for f1 in equation (VI).

f2=2(300.0Hz)=600.0Hz

The second lowest fundamental frequency of the standing wave is.

f4=4f1 (VII)

Substitute 300.0Hz for f1 in equation (VII).

f4=4(300.0Hz)=1200.0Hz=1.200×103Hz(103Hz1kHz)=1.200kHz

The third lowest fundamental frequency of the standing wave is.

f6=6f1 (VIII)

Substitute 300.0Hz for f1 in equation (VIII).

f6=6(300.0Hz)=1800.0Hz=1.800×103Hz(103Hz1kHz)=1.800kHz

The fourth lowest fundamental frequency of the standing wave is.

f8=8f1 (IX)

Substitute 300.0Hz for f1 in equation (IX).

f8=8(300.0Hz)=2400.0Hz=2.400×103Hz(103Hz1kHz)=2.400kHz

The pattern for the each situation for the four lowest standing wave frequencies is.

npatternnf1
2N    A    N    A    N600.0Hz
4N   A   N   A   N   A   N   A   N1.200kHz
6N  A  N  A  N  A  N  A  N  A  N  A  N1.800kHz
8NANANANANANANANAN2.400kHz

Therefore, the four lowest standing wave frequencies is f2=600.0Hz, f4=1.200kHz, f6=1.800kHz, and f8=2.400kHz.

(c)

To determine

The four lowest standing wave frequencies, when the strings press hard.

(c)

Expert Solution
Check Mark

Answer to Problem 74P

The four lowest standing wave frequencies is f1=600.0Hz, f2=1.200kHz, f3=1.800kHz, and f4=2.400kHz.

Explanation of Solution

The effective length of the string is now half of the original length.

Write the equation for lowest standing wave for fundamental frequency.

fn=nv2(L2) (X)

Here, fn is the new fundamental frequency for nth harmonic.

Rearrange the equation (X).

fn=nvL

Substitute equation (I) in above equation.

fn=2fn (XI)

Conclusion:

The first lowest fundamental frequency of the standing wave is.

f1=2(300.0Hz)=600.0Hz

The second lowest fundamental frequency of the standing wave is.

f2=2f2

Substitute 600.0Hz for f2.

f2=2(600.0Hz)=1.200kHz

The third lowest fundamental frequency of the standing wave is.

f3=2f3

Substitute 900.0Hz for f3.

f3=2(900.0Hz)=1800.0Hz=1.800×103Hz(103Hz1kHz)=1.800kHz

The fourth lowest fundamental frequency of the standing wave is.

f4=2f4

Substitute 1.200kHz for f4.

f4=2(1.200kHz)=2.400kHz

The pattern for the each situation for the four lowest standing wave frequencies is.

npatternfn=2fn
1N     A     N600.0Hz
2N    A    N    A    N1.200kHz
3N  A  N  A  N  A  N1.800kHz
4NANANANAN2.400kHz

Therefore, the four lowest standing wave frequencies is f1=600.0Hz, f2=1.200kHz, f3=1.800kHz, and f4=2.400kHz.

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Chapter 11 Solutions

PHYSICS

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