Final answer:
The frequency that could NOT produce a standing wave pattern on a string is 40 Hz, as it is not an integer multiple of the fundamental frequency, likely to be 30 Hz given that 60 Hz created a standing wave. Option b is the correct answer.
Step-by-step explanation:
The question posed involves understanding standing waves on a string and the resonance conditions required to produce them. When a frequency of 60 Hz is applied to a string fixed at both ends, it vibrates in a standing wave pattern. This 60 Hz is likely one of the harmonic frequencies of the string.
Harmonics on a string occur at integer multiples of the fundamental frequency. Given frequency 60 Hz, this suggests that the fundamental might be 30 Hz, and other modes would occur at higher integer multiples: 90 Hz, 120 Hz, etc. Therefore, frequencies like 40 Hz, 80 Hz, and 100 Hz would not align with these integer multiples and could not produce a standing wave pattern as these are not harmonics of 30 Hz.
Answer: Option b. 40 Hz could NOT produce a standing wave pattern on the string.