Question

Sinusoidal waves

5.00 cm

in amplitude are to be transmitted along a string that has a linear mass density of

4.00 \times 10^{- 2} kg / m .

. The source can deliver a maximum power of

300 W

and the string is under a tension of

100 N

. What is the highest frequency at which the source can operate?

Accepted Answer

Turning up the source, frequency will increase the power carried by the wave. Perhaps on the order of a hundred hertz will be the frequency at which the energy per second is $300 J / s$ .

We will use the expression for power carried by a wave on a string

The wave speed is $v = \sqrt{\frac{T}{μ}} = \sqrt{\frac{100 N}{4.00 \times 10^{- 2} kg / m}} = 50.0 m / s$

From $P = \frac{1}{2} μ ω^{2} A^{2} v$ , we have

$ω^{2} = \frac{2 P}{μ A^{2} v} = \frac{2 (3.00 N m / s)}{(4.00 \times 10^{- 2} kg / m) {(5.00 \times 10^{- 2} m)}^{2} (50.0 m / s)}$

Computing, $ω = 346.4 rad / s$ and $f = \frac{ω}{2 π} = 55.1 Hz$

This string wave would softly broadcast sound into the surrounding air, at the frequency of the second-lowest note called A on piano. If we tried to turn the source to a higher frequency, it might just vibrate with smaller amplitude. The power is generally proportional to the squares of both the frequency and the amplitude.

B M Sharma Solutions for Chapter: Travelling Waves, Exercise 1: ILLUSTRATIONS

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Travelling Waves, Exercise 1: ILLUSTRATIONS

Questions from B M Sharma Solutions for Chapter: Travelling Waves, Exercise 1: ILLUSTRATIONS with Hints & Solutions

Learn and Prepare for any exam you want !