The speed of a wave in a string is given by v = sqrt (FT/m), where FT is the tension in the string and m = mass / length of the string.

A 2.00 m long string has a mass of 28.50 g. A 1024 g mass is attached to the string and hung over a pulley (see illustration from one of the team problems). The end of the string is then vibrated at a frequency of 134 Hz. Find the wavelength for the wave generated. Give your answer in centimeters (cm) and with 3 significant figures.

To find the wavelength of the wave generated, we can use the formula:

wavelength (λ) = speed of the wave (v) / frequency (f)

Since we are given the frequency, we need to first find the speed of the wave using the given information.

The speed of the wave in the string can be calculated using the formula:

v = √(FT / m)

where FT is the tension in the string and m is the mass per unit length of the string.

Let's calculate the values step by step:

1. Convert the given mass of the string from grams to kilograms:

mass of the string = 28.50 g = 28.50 g / 1000 g/kg = 0.02850 kg

2. Calculate the mass per unit length of the string:

mass per unit length (m) = mass of the string / length of the string

= 0.02850 kg / 2.00 m

= 0.01425 kg/m

3. Calculate the speed of the wave:

v = √(FT / m)

We still need to find the tension in the string (FT). The tension is equal to the weight of the 1024 g mass attached to the string.

Tension in the string (FT) = weight of the mass

= mass of the mass x acceleration due to gravity

= (1024 g) x (9.8 m/s^2) = (1024 g) x (9.8 m/s^2) / 1000 g/kg

= 10.0352 N

Now we can substitute the values into the speed formula:

v = √(FT / m)

= √(10.0352 N / 0.01425 kg/m)

4. Calculate the speed of the wave:

v = √(10.0352 N / 0.01425 kg/m)

= √(703.22 m^2/s^2 / kg/m)

= √(703.22 m/s^2)

≈ 26.51 m/s

Now, we can use the calculated speed of the wave (v) and the given frequency (f) to find the wavelength (λ):

wavelength (λ) = v / f

= 26.51 m/s / 134 Hz

≈ 0.1977 m

To convert the wavelength from meters (m) to centimeters (cm), we multiply by 100:

wavelength in centimeters (cm) ≈ 0.1977 m x 100 cm/m

≈ 19.77 cm

Rounding to three significant figures, the wavelength is approximately 19.8 cm.