sir some physics question for waves

hello aspirant

following are some questions from ncert exemplar that you can solve:

1. A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be is resonance with the wire?
2. An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?
3. A tuning fork A, marked 512 Hz, produces 5 beats per second, where sounded with another unmarked tuning fork B. If B is loaded with wax the number of beats is again 5 per second. What is the frequency of the tuning fork B when not loaded?
4. The displacement of an elastic wave is given by the function
   y = 3 sin ωt + 4 cos ωt.
   where y is in cm and t is in second. Calculate the resultant amplitude.
5. A sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?
6. At what temperatures (in °C) will the speed of sound in air be 3 times its value at O°C?
7. When two waves of almost equal frequencies n ₁ and n ₂ reach at a point simultaneously, what is the time interval between successive maxima?
8. The pattern of standing waves formed on a stretched string at two instants of time are shown in Fig. 15.3. The velocity of two waves superimposing to form stationary waves is 360 ms ^–1 and their frequencies are 256 Hz.
   
   • (a) Calculate the time at which the second curve is plotted.
   • (b) Mark nodes and antinodes on the curve.
   • (c) Calculate the distance between A′ and C ′ .
9. The earth has a radius of 6400 km. The inner core of 1000 km radius is solid. Outside it, there is a region from 1000 km to a radius of 3500 km which is in molten state. Then again from 3500 km to 6400 km the earth is solid. Only longitudinal (P) waves can travel inside a liquid. Assume that the P wave has a speed of 8 km s ^–1 in solid parts and of 5 km s ^–1 in liquid parts of the earth. An earthquake occurs at some place close to the surface of the earth. Calculate the time after which it will be recorded in a seismometer at a diametrically opposite point on the earth if wave travels along diameter?
10. If c is r.m.s. speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.
11. Given below are some functions of x and t to represent the displacement of an elastic wave.
    • (a) y = 5 cos (4x ) sin (20t )
    • (b) y = 4 sin (5x – t/2) + 3 cos (5x – t/2)
    • (c) y = 10 cos [(252 – 250) πt ] cos [(252+250)πt ]
    • (d) y = 100 cos (100πt + 0.5x )
      State which of these represent
    • (a) a travelling wave along –x direction
    • (b) a stationary wave
    • (c) beats
    • (d) a travelling wave along +x direction.
      Given reasons for your answers
12. In the given progressive wave
    y = 5 sin (100πt – 0.4πx )
    where y and x are in m, t is in s. What is the

    
    

• (a) amplitude
• (b) wave length
• (c) frequency
• (d) wave velocity
• (e) particle velocity amplitude.

You can refer to the following links for more practice:

https://www.bbc.co.uk/bitesize/guides/zcjydxs/revision/1

https://www.saburchill.com/physics/questions/quest041.html

good luck! hope this helps