Two identical but separate strings, with the same tension, carry sinusoidal waves with the same frequency. Wave A has an amplitude that is twice that of wave B and transmits energy at a rate that is _____ that of wave B.
a)half
b)twice
c) one-fourth
d)four times
e) eight times
work:
I thought the answer was twice or b because a higher energy wave is characterized by a higher amplitude while a lower energy wave is characterized by a low amplitude.
A sinusoidal water waves are generated in a large ripple tank. The waves travel at 20cm/s and their adjacent crests are 5.0cm apart. The time required for each new whole cycle to be generated is.
a)100s
b)4.0s
c)2.0s
d)0.5s
e)0.25s
answer:
v=lambda *f
20 cm/s= (5.0cm)*f
f=4
T=1/4
T=.25s
Please check my answers and help point me in the right direction.
Thank you
option d
For the first question, your understanding is correct. The energy transmitted by a wave is directly related to its amplitude. Since wave A has twice the amplitude of wave B, it will transmit energy at a rate that is four times that of wave B. Therefore, the correct answer is (d) four times.
For the second question, your calculation is correct. The velocity of the wave is given by v = λ * f, where v is the velocity, λ is the wavelength, and f is the frequency. Since the adjacent crests are 5.0 cm apart and the velocity is 20 cm/s, we can solve for the frequency: 20 cm/s = (5.0 cm) * f. Thus, f = 4 Hz. The time required for each new whole cycle to be generated is the reciprocal of the frequency, which is 1/f, or 1/4 Hz. This is equivalent to 0.25s. Therefore, the correct answer is (e) 0.25s.
For the first question, you correctly determined that wave A has twice the amplitude of wave B. However, the energy transmitted by a wave is not directly proportional to its amplitude alone. The energy of a wave is proportional to the square of its amplitude.
Therefore, if wave A has an amplitude that is twice that of wave B, wave A actually transmits energy at a rate four times that of wave B. The correct answer is option d) four times.
For the second question, you correctly used the equation v = λ * f, where v is the wave velocity, λ is the wavelength, and f is the frequency. You found the wave velocity to be 20 cm/s and the distance between adjacent crests (wavelength) to be 5.0 cm.
To find the time required for each new whole cycle to be generated (period), you can use the relationship T = 1/f, where T is the period and f is the frequency. In this case, you already found f to be 4, so the period is T = 1/4 = 0.25 s.
Therefore, your answer for the second question is correct, which is option e) 0.25 s.
Overall, your work is mostly correct, except for the first question where you need to consider the square of the amplitude to determine the energy transmitted.