A wave on a string is described by the following equation (assume the +x direction is to the right).

y = (18 cm) cos[ðx/(5.3 cm) - ð t/(14 s)]

What is its period?
What is its speed?
In which direction does the wave travel? To the left or to the right?

for period, choose x=0. then when the second term is 2PI, t=period.

To find the period of the wave, we need to identify the coefficient in front of the "t" term. The equation for the wave is given as:

y = (18 cm) cos[ðx/(5.3 cm) - ð t/(14 s)]

From this equation, we can see that the period can be determined by looking at the coefficient in front of the "t" term, which in this case is ð/(14 s). The period (T) is defined as the time it takes for one complete cycle of the wave to occur. It is the reciprocal of the angular frequency (ω).

The angular frequency (ω) can be found by dividing 2π (since one complete cycle is equal to 2π radians) by the coefficient in front of the "t" term. Therefore, the angular frequency (ω) is:

ω = 2π/(ð/(14 s)) = 28 s^(-1)

To find the period (T), we take the reciprocal of the angular frequency:

T = 1/ω = 1/(28 s^(-1)) = 0.036 s

Therefore, the period of the wave is approximately 0.036 seconds.

Now let's find the speed of the wave. The wave speed (v) can be determined by dividing the wavelength (λ) by the period (T). In this equation, the wavelength (λ) can be found by identifying the coefficient in front of the "x" term, which in this case is ð/(5.3 cm).

The wave speed (v) can be calculated as:

v = λ/T = (ð/(5.3 cm))/0.036 s = ð/(5.3*0.036) cm/s

The wave speed is a positive value, and since the equation contains a cosine term, the wave travels in both positive and negative directions. However, the equation contains a negative sign in front of the "x" term, which indicates a displacement to the left. Therefore, the wave travels to the left.