A 4.0 Hz wave with an amplitude of 12 cm and a wavelength of 30.0 cm travels along a stretched horizontal string.

(a) How far does a given peak on the wave travel in a time interval of 6.0 s?
? m
(b) How far does a knot on the string travel in the same time interval?
? m

once again...lost my book :(

No problem! I can help you find the answers to your questions.

To find the distance traveled by a peak on the wave in a given time interval, we first need to calculate the wave speed. The wave speed can be obtained by multiplying the frequency (f) of the wave by the wavelength (λ). In this case, the frequency is 4.0 Hz and the wavelength is 30.0 cm.

(a) To find how far a peak travels in 6.0 s, we need to calculate the distance it covers. The formula for distance (d) is given by the equation: d = v * t, where v is the wave speed and t is the time interval.

First, we need to convert the wavelength from centimeters to meters, since the wave speed is usually measured in meters per second. So, we divide the wavelength by 100 to get 0.3 m.

The wave speed (v) can now be calculated by multiplying the frequency (f) by the wavelength (λ):
v = f * λ = 4.0 Hz * 0.3 m = 1.2 m/s

Now, we can calculate the distance (d) traveled by the peak using the formula:
d = v * t = 1.2 m/s * 6.0 s = 7.2 m

Therefore, the peak on the wave will travel 7.2 meters in 6.0 seconds.

(b) To find how far a knot on the string travels in the same time interval, we need to consider that the knot moves up and down as the wave passes through. The distance a knot travels is two times the amplitude of the wave because it moves full cycles (up and down) within a single wavelength.

In this case, the amplitude of the wave is given as 12 cm. We need to convert it to meters by dividing by 100, so the amplitude becomes 0.12 m.

Therefore, the distance a knot travels in the same time interval is:
2 * amplitude = 2 * 0.12 m = 0.24 m

So, a knot on the string will travel a distance of 0.24 meters in the time interval of 6.0 seconds.

Remember to check your calculations and units to ensure accurate answers.

Well, you have to get another book. I have no intention of working all your homework questions this semester.