1. The displacement associated with a wave is given by(i) ...(ii)
...(iii) ...where in each case x and y are measured in centimeters and t
in seconds. Calculate the wavelength, amplitude, frequency and the
velocity in each case. Get solution
2. A transverse wave (λ = 15 cm, ν = 200 sec –1 ) is propagating on a stretched string in the +x –direction with an amplitude of 0.5 cm. At t = 0 the point x = 0 is at its equilibrium position moving in the upward direction. Write the equation describing the wave and if ρ = 0.1 g/cm, calculate the energy associated with the wave per unit length of wire. Get solution
3. Assuming that the human ear can hear in the frequency range 20 Get solution
4. Calculate the speed of longitudinal waves at NTP in (a) argon (γ = 1.67), (b) Hydrogen (γ =1.41).[Ans : (a) 308 m/s, (b) 1.26×105 cm/s] Get solution
5. Consider a wave propagating in the +x-direction with speed 100 cm/sec. The displacement at x =10 cm is given by the following equationy(x =10, t) = 0.5 sin (0.4t) where x and y are measured in centimeters and t in seconds. Calculate the wavelength and the frequency associated with the wave and obtain an expression for the time variation of the displacement at x = 0. Get solution
6. Consider a wave propagating in the – x-direction whose frequency is 100 sec –1. At t =5 sec the displacement associated with the wave is given by the following equation:y(x, t = 5) = 0.5 cos (0.1x)where x and y are measured in centimeters and t in seconds. Obtain the displacement (as a function of x) at t = 10 sec. What is the wavelength and the velocity associated with the wave? Get solution
7. Repeat the above problem corresponding toy(x, t = 5) = 0.5 cos (0.1x) + 0.4 sin (0.1x + π/3) Get solution
8. A Gaussian pulse is propagating in the +x-direction and at t = t0 the displacement is given by...Find y(x, t). Get solution
9. A sonometer wire is stretched with a tension of 1 N. Calculate the velocity of transverse waves if ρ =0.2 g/cm. Get solution
10. The displacement associated with a three –dimensional wave is given by...Show that the wave propagates along a direction making an angle 30° with the x –axis. Get solution
11. Obtain the unit vector along the direction of propagation for a wave, the displacement of which is given by...where x, y and z are measured in centimeters and t in seconds. What will be the wavelength and the frequency of the wave?... Get solution
2. A transverse wave (λ = 15 cm, ν = 200 sec –1 ) is propagating on a stretched string in the +x –direction with an amplitude of 0.5 cm. At t = 0 the point x = 0 is at its equilibrium position moving in the upward direction. Write the equation describing the wave and if ρ = 0.1 g/cm, calculate the energy associated with the wave per unit length of wire. Get solution
3. Assuming that the human ear can hear in the frequency range 20 Get solution
4. Calculate the speed of longitudinal waves at NTP in (a) argon (γ = 1.67), (b) Hydrogen (γ =1.41).[Ans : (a) 308 m/s, (b) 1.26×105 cm/s] Get solution
5. Consider a wave propagating in the +x-direction with speed 100 cm/sec. The displacement at x =10 cm is given by the following equationy(x =10, t) = 0.5 sin (0.4t) where x and y are measured in centimeters and t in seconds. Calculate the wavelength and the frequency associated with the wave and obtain an expression for the time variation of the displacement at x = 0. Get solution
6. Consider a wave propagating in the – x-direction whose frequency is 100 sec –1. At t =5 sec the displacement associated with the wave is given by the following equation:y(x, t = 5) = 0.5 cos (0.1x)where x and y are measured in centimeters and t in seconds. Obtain the displacement (as a function of x) at t = 10 sec. What is the wavelength and the velocity associated with the wave? Get solution
7. Repeat the above problem corresponding toy(x, t = 5) = 0.5 cos (0.1x) + 0.4 sin (0.1x + π/3) Get solution
8. A Gaussian pulse is propagating in the +x-direction and at t = t0 the displacement is given by...Find y(x, t). Get solution
9. A sonometer wire is stretched with a tension of 1 N. Calculate the velocity of transverse waves if ρ =0.2 g/cm. Get solution
10. The displacement associated with a three –dimensional wave is given by...Show that the wave propagates along a direction making an angle 30° with the x –axis. Get solution
11. Obtain the unit vector along the direction of propagation for a wave, the displacement of which is given by...where x, y and z are measured in centimeters and t in seconds. What will be the wavelength and the frequency of the wave?... Get solution
