A pendulum clock keeps correct time at 20oC. The coefficient of linear expansion of pendulum is . If the room temperature increases to 40oC, how many seconds will the clock lose or gain per day?
The time period of a pendulum clock is given by
Partially differentiating we get
Dividing (ii) by (i) we have
Where α is the coefficient of linear expansion and âˆ†θ is the rise in temperature. Thus
Now, the time period of a pendulum clock T = 1s. Thus the clock gains 12 × 10–5 s every second. In a day (= 86400 s), the clock will gain 12 × 10–5× 86400 = 10.37 s.
If the amplitude of a sound wave is doubled and its frequency reduced to one-fourth, the intensity of sound at the same point will
At a certain instant a stationary transverse wave is found to have maximum kinetic energy. The appearance of the string at that instant is a
The displacement y of a particle executing simple harmonic motion is given by
The expression may be considered to be a result of the superposition of how many simple harmonic motions?
A wave of frequency 100 Hz is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of 10 cm from the fixed end of the string. The speed of the incident (or reflected) wave is
A particle starts simple harmonic motion from the mean position O as shown in the figure. Its amplitude is A and its time period is T. At a certain instant, its speed is half its maximum speed. At this instant, the displacement x is
The wave equation is
Where t, x and y are in second, metre and centimeter respectively. The speed of the wave is
An observer is standing between two vehicles, each moving with a speed 4 ms–1. One vehicle is approaching him and the other going away from him. If each vehicle is blowing a horn of frequency 240 Hz and the speed of sound is 320 ms–1, the number of beats per second will be
A spring is extended by a length l, the according to Hooke’s law
A transverse wave is represented by
For what value of λ is the maximum particle velocity equal to twice the wave velocity?
A mass m is suspended from a spring of negligible mass. The system oscillates with frequency n. What will be the frequency if a mass 4 m is suspended from the same spring?