Answer:
[tex]f_5=750 \ Hz[/tex]
Conception:
What is a standing wave? A standing wave is a wave produced by two interfering waves which creates a unique shape that almost makes the wave look stationary. Standing waves can also be referred to as stationary waves (refer to the attached image).
Two distinct points exist on standing waves called nodes and antinodes. A node occurs where there is no displacement from equilibrium which is caused by complete destructive interference. An antinode occurs where there is max displacement from equilibrium which is caused by complete constructive interference(refer to the attached image).
What is frequency? The frequency of a wave is the number of waves that pass a fixed point per second. The unit of measurement for frequency is one cycle per second which is a hertz, "Hz."
Explanation:
Given that a string is vibrated at 600 Hz creates a standing wave with four antinodes. Find at what frequency will create a standing wave with five antinodes.
We first need to find the fundamental frequency, which is the lowest frequency possible to create a standing wave.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Use the formula:}}\\f_n=nf_1\\\end{array}\right }[/tex]
"f_1" represents the fundamental frequency. Find "f_1."
[tex]\Longrightarrow f_n=nf_1;f_4=600 \ Hz;n=4\\\\\Longrightarrow 600=(4)f_1 \Longrightarrow f_1=\frac{600}{4} \Longrightarrow \boxed{f_1=150 \ Hz}[/tex]
Use the fundamental frequency to find the frequency to produce a standing wave with five antinodes. We are now finding "f_5."
[tex]\Longrightarrow f_5=(5)f_1 \Longrightarrow f_5=(5)(150) \Longrightarrow \boxed{\boxed{\therefore f_5=750 \ Hz}}[/tex]
Thus, the frequency to produce a standing wave with 5 antinodes is found.
