Question

FOCUS ONLY ON QUESTION d) THAN K YOU

Sketch a plot of a sinusoidal wave as a function of time and mark on the plot the amplitude, period and the point at which the particles involved in the wave disturbance have the highest velocity.
b) (3 marks) Write down the mathematical form for the wave of amplitude A propagating in the positive x direction with a speed 5 ms-1 and wavelength  = 1.4 m.
c) (4 marks) Provide an example of a transverse wave and one for a longitudinal wave. Use these to describe the nature of the wave disturbance in each case.
d) An open-ended pipe contains a plunger so that the length of the closed-open pipe can be varied. The sound wave has frequency 2.1 kHz.
(i) (4 marks) As the pipe length is increased from zero, what are the first 3 lengths that produce a standing wave?
(ii) (2 marks) Draw the standing wave patterns in each case.
(iii) (4 marks) The speed of sound varies increases with √? where T is the temperature of the air in Kelvin. Consider two identical pipes resonating at their 4th harmonic frequency at 300 K. By how many degrees would you need to increase the temperature of one pipe to produce a beat frequency of 8.0 Hz?

Answer 1

of with mode i) 2 wave length one - closed The of the 2 l pipe és ant n+/ m=0,1,2-- e = length of the pipe ex (M+Y2) ze - frequency do C an of with velocity of mod serend, here Do = 2.1 kHz l= cx (n+/ 2 Dn ist length for n=o mode c C cx zon 2 e 4x2.1 c= 343 m/s 40.83 m LU m = 0 < 21 = 40.83m> N=1 i) 2nd length e (1/2) = 122.5 m 3 43 x 3 482.1 2 un n = - 122.5m

Now n = 2 for (2+₂) 2 in 5c 5x 343 4x2.1 = 204.16 m iz) e=204.16m ใน frequency e(n+/ 2 l ) → Саут De ac » un art T constant endependent of temps. → 1st pipe KT2 - 2nd pipe » ال2 i = Kit 4. = 2.1 H3 - at I'= 3ook 8.03 22 T Ja? √ 77 3 572 = JT ( 22 ) T' () Book Book * ( ) T = = 43 5374K

T² = 4353.74k one need to increase tempo leef amount = 62-T') on tegrees 4053.74 degrees.