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

A standing wave is produced on a string fixed at one end with the other end free. The length of the string _____.

The equation of a simple harmonic progressive wave is given by, y = 5cosπ`[200t - x/150]`, where x and y are in cm and ‘t’ is in second. Then the velocity of the wave is ______.

A man standing unsymmetrical position between two mountains and fires a gun. He hears the first echo after 1.5 s and the second echo after 2.5 s. If the speed of sound in air is 340 m/s, then the distance between the mountains will be ______ 

A set of tuning forks is arranged in ascending order of frequencies each tuning fork gives 8 beats/s with the preceding one. If the frequency of the first tuning fork is 120 Hz and the last fork is 200 Hz, then the number of tuning forks arranged will be, ______ 

In the law of tension, the fundamental frequency of the vibrating string is, ______   

The integral multiple of fundamental frequencies are ______ 

An organ pipe of length 0.4 m is open at both ends. The speed of sound in the air is 340 m/s. The fundamental frequency is ______ 

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? 

Why wave motion is doubly periodic?

What is the interference of sound waves? 

What are beats?

What are harmonics? 

What are overtones?

State law of length.

State law of tension.

State law of linear density.

What is the resonance?

What are forced vibrations? 

A violin string vibrates with the fundamental frequency of 510 Hz. What is the frequency of the first overtone? 

A string 1 m long is fixed at one end. The other end is moved up and down with a frequency of 20 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. 

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

What are stationary waves? Why are they called stationary waves? 

Distinguish between an overtone and harmonic. 

State any four applications of beats.

Prove that a pipe open at both ends of a length of 2L has the same fundamental frequency as another pipe of closed at one end of length L.

How the frequency of the vibrating wire is affected if the load is fully immersed in water? 

A sonometer wire of length 1 m is stretched by a weight of 10 kg. The fundamental frequency of vibration is 100 Hz. Determine the linear density of the material of the wire.

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

Show that even as well as odd harmonics are present as an overtone in modes of vibration of the string. 

State the laws of vibrating strings

Two wires of the same material and same cross-section are stretched on a sonometer. One wire is loaded with 1 kg and another is loaded with 9 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. 

The equation of simple harmonic progressive wave is, y = sin π/2 (4t/0.025 – x/0.25). Where all quantities are in the S.I. system. Find the amplitude, frequency, wavelength, and velocity of the wave.

A stretched sonometer wire is in unison with a tuning fork. When the length is increased by 4%, the number of beats heard per second is 6. Find the frequency of the fork.

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

What are nodes?

What are antinodes?

Show that the distance between two successive nodes or antinodes is λ/2.

Explain the production of beats and deduce analytically the expression for beats frequency.

State and verify the laws of vibrating strings using a sonometer. 

Waves produced by two vibrators in a medium have wavelength 2 m and 2.1 m respectively. When sounded together they produce 8 beats/second. Calculate wave velocity and frequencies of the vibrators.