A continuous succession of sinusoidal wave pulses are produced at one end of a v

Question

A continuous succession of sinusoidal wave pulses are produced at one end of a very long string and travel along the length of the string. The wave has frequency 55.0 Hz , amplitude 4.95 mm , and wavelength 0.645 m .

question A:How long does it take the wave to travel a distance of 7.70 m along the length of the string?

question B:How long does it take a point on the string to travel a distance of 7.70 m , once the wave train has reached the point and set it into motion?

question C:In parts (a) and (b), how does the time change if the amplitude is doubled? (what is T_a/T_c and T_b/T_c)

Explanation / Answer

a)

Speed = wavelength x frequency

= 0.645* 55

= 35.475 m/s
Time = distance/speed

= 7.7/ 35.475

= 0.217 s

---------------------------------------------------------------------------------

b)

Distance per cycle = 4 * amplitude
= 4 x 4.95X10-3

= 19.8 mm

= 0.0198 m

Number of cycles:

n = 7.7/0.0198 = / 0.0218 = 388.89 cycles

hence, the period: T = 1/f = 1/55 = 0.01818 s

Time taken is

t = nT = 388.89 x 0.01818

= 7.07 s

C.

Time is directly proportional to amplitude.

So, the time is also doubled when the amplitude is doubled.

T_a/T_c = 1 and T_b/T_c = 2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.