To solve this problem we will apply the concepts related to the wavelength of its third harmonic.
It describes that the wavelength is equivalent to
Here,
The wavelength is in turn described as a function that depends on the change of the speed as a function of the frequency, that is to say
In this case the speed is equivalent to the speed of sound and the frequency was previously given, therefore
Finally the length of the pipe would be
Answer:
(a) The length of the pendulum on Earth is 36.8cm
(b) The length of the pendulum on Mars is 13.5cm
(c) Mass suspended from the spring on Earth is 0.37kg
(d) Mass suspended from the spring on Mars is 0.36kg
Explanation:
Period = 1.2s, free fall acceleration on Earth = 9.8m/s^2, free fall acceleration on Mars = 3.7m/s^2
( a) Length of pendulum on Earth = [( period ÷ 2π)^2] × acceleration = (1.2 ÷ 2×3.142)^2 × 9.8 = 0.0365×9.8 = 0.358m = 35.8cm
(b) Length of the pendulum on Mars = (1.2÷2×3.142)^2 × 3.7 = 0.0365×3.7 = 0.135cm = 13.5m
(c) Mass suspended from the spring on Earth = (force constant×length in meter) ÷ acceleration = (10×0.358) ÷ 9.8 = 0.37kg
(d) Mass suspended from the spring on Mars = (10×0.135)÷3.7 = 0.36kg
The answer is 570 J. The kinetic energy has the formula of 1/2mV². The total work in this process W= 1/2m(V2²-V1²) = 1/2 * 15.0 * (11.5²-7.50²) = 570 J.
