SPH102 Make-up CAT March 2023 SOLVED

(1) A simple harmonic wave is represented by

 . 

The time period is 30 s. At time t=0, the displacement is 5 cm. Calculate the phase angle (2πt/2 +φ) at t=7.5 s

To find the value of φ, use boundary condition y= 5cm at t=0

Phase angle at t=7.5 s, T=30 s

(2) A tuning fork A of frequency 384 Hz gives 6 beats per second when sounded with another tuning fork B. On loading B with a little wax, the number of beats per second become 4. What is the frequency of B?           

either                                                                                                                     

or

When f_B is loaded with a little wax, the beat frequency reduces. This can only happen if B had a higher frequency relative to A (since loading reduces frequency) hence;

(3)A guitar wire of length 80 cm is under a tension of 30 N. A 10 m sample of that wire has a mass of 2.2 g. Find; 

(a)The speed of the transverse waves on the wire                                                        

(b) The fundamental frequency                 

(4) A train travelling at 45 km/h produces a whistling sound of frequency 600 Hz. Another train approaches this train on a parallel rail and a person in the second train hears the whistling of the first trains as sound of frequency 800 Hz. Find the speed of the second train. Assume the velocity of sound = 340 m/s.                          

f=600 Hz

f’=800 Hz     

v=340 m/s   

Dr. Margaret W. Chege