A plane sound wave is travelling in a medium. In a reference frame A fixed to the medium , its equation is y = a cos(ωt − kx ) . With respect to reference frame B, moving with a constant velocity v in the direction of propagation of the wave, equation of the wave will be
A sinusoidal wave is generated by moving the end of a string up and down, periodically. The generator must apply the energy at maximum rate when the end of the string attached to generator has X and least power when the end of the string attached to generator has Y. The most suitable option which correctly fills blanks X and Y, is
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A stationary observer receives sonic oscillations from two tuning forks, one of which approaches and the other recedes with same speed. As this takes place the observer hears the beat frequency of 2 Hz. Find the speed of each tuning fork,(assuming it is very small when compared to sound) if their oscillation frequency is 680 Hz and the velocity of sound in air is 340 m/s.
A string of length 1.5 m with its two ends clamped is vibrating in fundamental mode. Amplitude at the centre of the string is 4 mm. Distance between the two points having amplitude 2 mm is:
A string of length ℓ is fixed at both ends. It is vibrating in its 3rd overtone with maximum amplitude ‘a’. The amplitude at a distance l /3 from one end is :
The figure shows at time t = 0, a rectangular and triangular pulse on a uniform wire are approaching each other. The pulse speed is 0.5 cm/s. The resultant pulse at t = 2 second
is
Four waves are described by equations as follow
and their resultant wave is calculated as Y = Y1 + Y2 + Y3 + Y4 such as Y = A1 cos ( ωt − kx + φ ) then………..(symbols have their usual meanings)
A 100 m long rod of density 10.0 x 104 kg/m3 and having Young’s modules Y = 1011 Pa, is clamped at one end. It is hammered at the other free end. The longitudinal pulse goes to right end, gets reflected and again returns to the left end. How much time, the pulse take to go back to initial point.
An aluminium wire of length 60cm is joined to a steel wire of length 80 cm and stretched between two fixed supports.
The tension produced is 40 N. The cross – sectional areas of the steel and aluminium wires are 1.0mm2 and 3.0mm2 respectively. The densities of steel and aluminium are 7.8 g / cm3 and 2.6 g / cm3 respectively. The frequency of first overtone of this composite wire with the joint as a node is nearly
Figure shown is a graph, at a certain time t, of the displacement function S ( x, t ) of three sound waves 1,2 and 3 as marked on the curves that travel along x-axis through air. If P1, P2 and P3 represent their pressure oscillation amplitudes respectively, then correct relation between them is:
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