Did you find an example that works that way ? Is it, for example, allowed that the TCNT1 is cleared in an interrupt routine? The TCCR1A is cleared, but not set to a value ?
The calculation uses a long of 2MHz, but the others are 16 bits. Could you force that calculation with long ? f = int( 2000000L / long( TCNT1));
The 'f' variable is used in an interrupt and outside that interrupt. It must be made 'volatile': volatile int f=0;
The 'f' is used in the loop, but the interrupt could happen when 'f' is only half read or half written. The ATmega328P is a 8-bit microcontroller and 'f' is a 16-bits variable. I suggest to disable the interrupts and make a copy.
noInterrupts();
int fcopy = f;
interrupts();
sprintf(msg,"Humidity:%d \n",fcopy);
What is the range that you want to measure ?
Do you know that there are good libraries to measure a frequency ? They are the FreqMeasure Library and the FreqCount Library.
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Try to slow down the loop with a delay. If you fill the transmit buffer of the Arduino Uno TX, then the Serial.println wait for each character if there is a place in the transmit buffer.