A certain string will resonante to several frequencies , the lowest of which is 200 cps. What are the next three higher frequencies to which it resonantes ?

Options

A. 400 , 600 , 800
B. 300 , 400 , 500
C. 100 , 150 , 200
D. 200 , 250 , 300

Answer

To find the next three higher frequencies to which a certain string resonates, we start with the information given in the question.

### Step-by-Step Solution:

1. **Identify the Fundamental Frequency**:
The lowest frequency at which the string resonates is given as 200 cycles per second (cps). This is also known as the fundamental frequency (f1).
\[ f_1 = 200 \text{ cps} \]

2. **Calculate the Second Harmonic Frequency**:
The second harmonic frequency (f2) is twice the fundamental frequency.
\[ f_2 = 2 \times f_1 = 2 \times 200 = 400 \text{ cps} \]

3. **Calculate the Third Harmonic Frequency**:
The third harmonic frequency (f3) is three times the fundamental frequency.
\[ f_3 = 3 \times f_1 = 3 \times 200 = 600 \text{ cps} \]

4. **Calculate the Fourth Harmonic Frequency**:
The fourth harmonic frequency (f4) is four times the fundamental frequency.
\[ f_4 = 4 \times f_1 = 4 \times 200 = 800 \text{ cps} \]

5. **List the Results**:
The next three higher frequencies after the fundamental frequency of 200 cps are:
- Second harmonic: 400 cps
- Third harmonic: 600 cps
- Fourth harmonic: 800 cps

### Final Answer:
The next three higher frequencies are:
- 400 cps
- 600 cps
- 800 cps