Wave Amplitude and Knot Movement

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A 4.0 Hz wave with a 12 cm amplitude and a 30.0 cm wavelength travels 3.6 m in 3.0 seconds. To determine how far a knot on the string moves in that time, it's important to note that the knot reaches its amplitude peak four times per second. Over 3 seconds, the knot oscillates a total of 12 times (4 peaks per second multiplied by 3 seconds). Since the maximum displacement is 12 cm, the total vertical distance traveled by the knot is 12 cm multiplied by 12 oscillations, resulting in a total movement of 144 cm. Understanding wave motion and amplitude is crucial for calculating knot movement accurately.
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A 4.0 Hz wave with an amplitude of 12 cm and a wavelength of 30.0 cm travels along a stretched string.

(a) How far does the wave travel in a time interval of 3.0 s?
m

(b) How far does a knot on the string travel in the same time interval?
m


I got the answer to part (a) by using: x= lambda x (time/frequency)
The answer I got for it was 3.6 m.
I don't know what to do for part (b) Something to do with the amplitude, but I'm not sure...pls help! Thanks!
 
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Consider that a knot on the string reaches its amplitude peak four times each second. (also remember that a point on a string is not displaced horizontally when the string undergoes wave motion).
 
ok...so, how would I figure (b) out? Since the amplitude is reached 4 times in a second, and the time interval is 3 seconds, and the amplitude is 12 cm, how would you figure out the distance traveled?
 
Just a small refrase of your last message:

you reach the amplitude of 12 cm 4 times per second for an interval of 3 seconds...

This might enable you to see the answer...

Regards,
Leo
 
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