Chapter 17: Q. 79 (page 487)

When mass $M$ is tied to the bottom of a long, thin wire suspended from the ceiling, the wire's second-harmonic frequency is $200 Hz$ Adding an additional $1.0 kg$ to the hanging mass increases the second-harmonic frequency $245 Hz$ . What is $M$ ?

Short Answer

Expert verified

The suspended mass is $2$ kg.

Step by step solution

Given information

Second harmonic frequency when mass $M$ is suspended $f = 200 Hz .$

When is suspended, $f^{'} = 245 Hz$ (second harmonic frequency)

Length of wire $L =$ (same for both frequencies as the same wire is used for both masses) $μ =$ (Same for both frequencies as the same wire is used)

Formula:

$f = \frac{1}{L} \sqrt{\frac{T}{μ}} \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots . .$

(General frequency for the second harmonic)

$T = M a s s x g r a v i t y . . . . . . . . . . . . . . . . . . . . . . . . .$

(Tension in the wire due to suspended masses)

Calculation

(I) When the mass $' M'$ is suspended

$f = \frac{1}{L} \sqrt{\frac{T}{μ}} 200 = \frac{1}{L} \sqrt{\frac{M_{g}}{μ}}$

Both sides are squaring up

$40000 = \frac{1}{L^{2}} \frac{M_{R}}{μ}$

(II) when the mass $' M + 1'$ is suspended.

$f^{'} = \frac{1}{L} \sqrt{\frac{T}{μ}}$

$245 = \frac{1}{L} \sqrt{\frac{(M + I)}{μ}}$

Both sides are squaring up

$60025 = \frac{1}{L^{2}} \frac{(M + 1) g}{μ}$

Dividing equation (I) from equation (II)

We compute that the initial mass hanging from the wire is $2$ kg using both frequencies.

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When mass $M$ is tied to the bottom of a long, thin wire suspended from the ceiling, the wire's second-harmonic frequency is $200 Hz$ Adding an additional $1.0 kg$ to the hanging mass increases the second-harmonic frequency $245 Hz$ . What is $M$ ?

Short Answer

Step by step solution

Given information

Calculation

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When mass Mis tied to the bottom of a long, thin wire suspended from the ceiling, the wire's second-harmonic frequency is200HzAdding an additional1.0kgto the hanging mass increases the second-harmonic frequency245Hz. What is M?

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Atoms and Radioactivity

Wave Optics

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Study anywhere. Anytime. Across all devices.

When mass $M$ is tied to the bottom of a long, thin wire suspended from the ceiling, the wire's second-harmonic frequency is $200 Hz$ Adding an additional $1.0 kg$ to the hanging mass increases the second-harmonic frequency $245 Hz$ . What is $M$ ?