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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Wave Motion and Waves on a String

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Wave Motion and Waves on a String

A string, 2 m long and fixed at both ends, is set into vibrations...

A string,

2 \text{ m}

long and fixed at both ends, is set into vibrations in its first overtone. The wave speed on the string is

200 \text{ m s}^{-1}

and the amplitude is

0.5 \text{ cm}

. Determine the wavelength and the frequency.

Options

A $2 \text{ m}$ , $100 \text{ Hz}$
B $4 \text{ m}$ , $50 \text{ Hz}$
C $1 \text{ m}$ , $200 \text{ Hz}$
D $\dfrac{4}{3} \text{ m}$ , $150 \text{ Hz}$

Correct answer

A. $2 \text{ m}$ , $100 \text{ Hz}$

Step-by-step solution

For a string of length

L

fixed at both ends, the wavelength of the

n

-th harmonic is given by

\lambda = \dfrac{2L}{n}

.

The first overtone corresponds to the second harmonic, so

n = 2

.

Substituting

L = 2 \text{ m}

and

n = 2

:

\lambda = \dfrac{2 \times 2}{2} = 2 \text{ m}

The frequency of the wave is given by

f = \dfrac{v}{\lambda}

.

Given the wave speed

v = 200 \text{ m s}^{-1}

:

f = \dfrac{200}{2} = 100 \text{ Hz}

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