A 3m slinky rests on a table with a student holding each end. The students laterally shake the ends of the slinky to generate transverse waves. The student on the left shakes the slinky at 4Hz with a 5cm amplitude and the student on the right shakes it at 3Hz with a 7cm amplitude.
The question asks what student's wave travels the fastest?
A. Left
B. Right
C. Same(correct)
D. More information is needed
My question is how can the two travel at the same speed? We do not know wavelength
C. Because the waves are traveling through the same medium.
Do the waves generated on the left side of a piano keyboard travel at a different speed through the air than those on the right side?
v = wavelength / period
If you cut the wavelength in half, the frequency doubles and the period (1/f) is cut in half. The speed ratio = 1/2 / 1/2 = 1
To determine which student's wave travels the fastest, we need to compare their wave speeds. The wave speed can be calculated using the formula:
Wave speed = frequency × wavelength
While we do not know the exact wavelength, we can deduce that both students are shaking the slinky laterally and generating transverse waves. In transverse waves, the wavelength is typically the distance between two consecutive crests or troughs of the wave.
Since both students are shaking the same slinky, the wavelength would generally remain the same for both of them. Therefore, if the frequency is different, the wave speed will be different as well.
Given that the student on the left shakes the slinky at 4Hz and the student on the right shakes it at 3Hz, we can conclude that their frequencies are unequal.
Since frequency is directly proportional to wave speed, the wave generated by the student with a higher frequency (4Hz) will travel faster.
Therefore, the student on the left generates a wave that travels faster than the student on the right.
Hence, the correct answer is A. Left.
To determine which student's wave travels the fastest, we need to consider the speed of the wave. In this case, the speed of the wave can be determined by the product of the frequency and the wavelength.
Since the question does not provide the wavelength for either student's wave, we cannot directly compare their speeds. The speed of a wave depends on the medium through which it is traveling and the properties of the wave, such as its frequency and wavelength.
However, we can make an assumption that the medium through which the wave is traveling and the properties of the wave are the same for both students. If this assumption is correct, then we can compare the speeds of the waves based solely on their frequencies.
The speed of the wave is directly proportional to its frequency. A wave with a higher frequency will travel faster than a wave with a lower frequency, assuming all other factors are the same. Therefore, the student with a higher frequency, which is 4Hz, shakes the slinky faster, indicating that their wave travels faster.
Hence, the correct answer is B. Right, as the wave generated by the student on the right travels faster based on their higher frequency.