Balbharati solutions for Physics [English] 12 Standard HSC Maharashtra State Board chapter 6 - Superposition of Waves [Latest edition]

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When an air column in a pipe closed at one end vibrates such that three nodes are formed in it, the frequency of its vibrations is  _____ times the fundamental frequency.

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If two open organ pipes of length 50 cm and 51 cm sounded together produce 7 beats per second, the speed of sound is ______.

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The tension in a piano wire is increased by 25%. Its frequency becomes ______ times the original frequency.

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Which of the following equations represents a wave travelling along Y-axis? 

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A standing wave is produced on a string clamped at one end and free at the other. The length of the string ______.

Answer in brief:

A wave is represented by an equation y = A sin (Bx + Ct). Given that the constants A, B and C are positive, can you tell in which direction the wave is moving?

Answer in brief:

A string is fixed at the two ends and is vibrating in its fundamental mode. It is known that the two ends will be at rest. Apart from these, is there any position on the string which can be touched so as not to disturb the motion of the string? What will be the answer to this question if the string is vibrating in its first and second overtones? 

Answer in brief:

What are harmonics and overtones?

Answer in brief.

For a stationary wave set up in a string having both ends fixed, what is the ratio of the fundamental frequency to the second harmonic?

Answer in brief.

The amplitude of a wave is represented by y = 0.2 sin 4π `["t"/0.08-"x"/0.8]` in SI units. Find (a) wavelength, (b) frequency, and (c) amplitude of the wave.

State the characteristics of progressive waves.

Answer in brief:

State the characteristics of stationary waves.

Derive an expression for the equation of stationary wave on a stretched string.

Find the amplitude of the resultant wave produced due to interference of two waves given as y₁ = A₁ sinωt, y₂ = A₂ sin(ωt + φ)

State the laws of vibrating strings

Explain how vibrating strings can be verified using a sonometer.

Show that only odd harmonics are present in an air column vibrating in a pipe closed at one end.

With a neat labelled diagram, show that all harmonics are present in an air column contained in a pipe open at both the ends. Define end correction.

A wave of frequency 500 Hz is traveling with a speed of 350 m/s. (a) What is the phase difference between two displacements at a certain point at times 1.0 ms apart? (b) what will be the smallest distance between two points which are 45° out of phase at an instant of time?

A sound wave in a certain fluid medium is reflected at an obstacle to form a standing wave. The distance between two successive nodes is 3.75 cm. If the velocity of sound is 1500 m/s, find the frequency.

Two sources of sound are separated by a distance of 4 m. They both emit sound with the same amplitude and frequency (330 Hz), but they are 180° out of phase. At what points between the two sources, will the sound intensity be maximum?

Two sound waves travel at a speed of 330 m/s. If their frequencies are also identical and are equal to 540 Hz, what will be the phase difference between the waves at points 3.5 m from one source and 3 m from the other if the sources are in phase?

Two wires of the same material and the same cross-section are stretched on a sonometer. One wire is loaded with 1.5 kg and another is loaded with 6 kg. The vibrating length of the first wire is 60 cm and its fundamental frequency of vibration is the same as that of the second wire. Calculate the vibrating length of the other wire.

A pipe closed at one end can produce overtones at frequencies 640 Hz, 896 Hz, and 1152 Hz. Calculate the fundamental frequency.

A standing wave is produced in a tube open at both ends. The fundamental frequency is 300 Hz. What is the length of the tube? (speed of the sound = 340 m s^-1).

Find the fundamental, first overtone, and second overtone frequencies of a pipe, open at both the ends, of length 25 cm if the speed of sound in air is 330 m/s.

A pipe open at both the ends has a fundamental frequency of 600 Hz. The first overtone of a pipe closed at one end has the same frequency as the first overtone of the open pipe. How long are the two pipes?

(Given: v = 330 m/s)

A string 1m long is fixed at one end. The other end is moved up and down with frequency of 15 Hz. Due to this, a stationary wave with four complete loops gets produced on the string. Find the speed of the progressive wave which produces the stationary wave.
[Hint: Remember that the moving end is an antinode.]

A violin string vibrates with fundamental frequency of 440Hz. What are the frequencies of the first and second overtones?

A set of 8 tuning forks is arranged in a series of increasing order of frequencies. Each fork gives 4 beats per second with the next one and the frequency of last fork is twice that of the first. Calculate the frequencies of the first and the last fork.

A sonometer wire is stretched by the tension of 40 N. It vibrates in unison with a tuning fork of frequency 384 Hz. How many numbers of beats get produced in two seconds if the tension in the wire is decreased by 1.24 N?

A sonometer wire of length 0.5 m is stretched by a weight of 5 kg. The fundamental frequency of vibration is 100 Hz. Calculate the linear density of wire.

The string of a guitar is 80 cm long and has a fundamental frequency of 112 Hz. If a guitarist wishes to produce a frequency of 160 Hz, where should the person press the string?