# Finding gravity on Planet X from a string, a weight, and frequency

LBRRIT2390

## Homework Statement

Astronauts visiting Planet X have a 2.5 m-long string whose mass is 5.0 g. They tie the string to a support, stretch it horizontally over a pulley 1.8 m away, and hang a 1.3 kg mass on the free end. Then the astronauts begin to excite standing waves on the string. Their data show that standing waves exist at frequencies of 64 Hz and 80 Hz, but at no frequencies in between.

What is the value of g, the acceleration due to gravity, on Planet X?

## Homework Equations

Fundamental frequency of a stretched string
f1=$$\frac{1}{2L}$$$$\sqrt{\frac{T_s}{\mu}}$$

Linear Density of a string
$$\mu$$ = $$\frac{mass}{length}$$

## The Attempt at a Solution

Ts = 1.3kg(g)

$$\mu$$ = $$\frac{0.005kg}{2.5m}$$ = 0.002

L = 1.8m

f1 = 64Hz

Place in Fundamental frequency equation and solve for g.

64Hz=$$\frac{1}{2(1.8m)}$$$$\sqrt{\frac{1.3*g}{0.002}$$

for f1 = 64Hz, I got g = 81

I tried substituting different frequencies and using a different L but I could not arrive at the correct answer which is g=5 m/s2

Can someone please teach me how to arrive at this correct answer?