Sinusoidal waves 5 . 00 cm in amplitude are to be transmitted along a string that has a linear mass density of 4 . 00 × 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?

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 = T μ = 100 N 4 . 00 × 10 - 2 kg / m = 50 . 0 m / s From P = 1 2 μ ω 2 A 2 v , we have ω 2 = 2 P μ A 2 v = 2 ( 3 . 00 N m / s ) 4 . 00 × 10 - 2 kg / m 5 . 00 × 10 - 2 m 2 ( 50 . 0 m / s ) Computing, ω = 346 . 4 rad / s and f = 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.

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Transverse waves travel with a speed of $20.0 m / s$ in a string under a tension of $6.00 N$ . What tension is required for a wave speed of $30.0 m / s$ in the same string?

Important Questions on Travelling Waves

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 6 - Travelling Waves>ILLUSTRATIONS>Q 6.27

A rope of total mass m and length L is suspended vertically. Find the time taken by a transverse pulse travels the length of the rope.

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Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 6 - Travelling Waves>ILLUSTRATIONS>Q 6.28

An aluminium wire is clamped at each end and under zero tension at room temperature. Reducing the temperature, which results in a decrease in the wire's equilibrium length, increases the tension in the wire. What strain

(Δ L / L)

results in a transverse wave speed of

100 m / s

? Take the cross-sectional area of the wire to be

5.00 \times 10^{- 6} m^{2}

, the density to be

2.70 \times 10^{3} kg / m^{3}

, and Young's modulus to be

7.00 \times 10^{10} N / m^{2}

MEDIUM

Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 6 - Travelling Waves>ILLUSTRATIONS>Q 6.29

A transverse wave of wavelength

50 cm

is travelling towards +ve

x

-axis along a string whose linear density is

0.05 g / cm

. The tension in the string is

450 N

. At

t = 0

, the particle at

x = 0

is passing through its mean position with an upward velocity. Form an equation describing the wave. The amplitude of the wave is

2.5 cm

HARD

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 6 - Travelling Waves>ILLUSTRATIONS>Q 6.30

Figure represents two snaps of a travelling wave on a string of mass per unit length $μ = 0.25 kg / m$ . The first snap is taken at $t = 0$ and the second is taken at $t = 0.05 s$ . Determine (a) the speed of the wave, (b) the wavelength and frequency of the wave, (c) the maximum speed of the particle, (d) the tension in the string (e) the equation of the wave.

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HARD

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 6 - Travelling Waves>ILLUSTRATIONS>Q 6.31

A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is

v

. If a small transverse disturbance is produced at a point of the loop, with what speed (relative to the string) will this disturbance travel on the string?

HARD

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 6 - Travelling Waves>ILLUSTRATIONS>Q 6.32

A taut string for which

μ = 5.00 \times 10^{- 2} kg m^{- 1}

is under a tension of

80.0 N

. How much power must be supplied to the string to generate sinusoidal waves at a frequency of

60.0 Hz

and an amplitude of

6.00 cm

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 6 - Travelling Waves>ILLUSTRATIONS>Q 6.33

Two waves in the same medium are represented by $y - t$ curves in the figure. Find the ratio of their average intensities?

Question Image

HARD

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 6 - Travelling Waves>ILLUSTRATIONS>Q 6.34

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?

Transverse waves travel with a speed of 20.0 m/s in a string under a tension of 6.00 N. What tension is required for a wave speed of 30.0 m/s in the same string?

Important Questions on Travelling Waves

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Transverse waves travel with a speed of $20.0 m / s$ in a string under a tension of $6.00 N$ . What tension is required for a wave speed of $30.0 m / s$ in the same string?